the height of the firecracker after 4 seconds from launch is 68 feet.
To find the height of the firecracker after 4 seconds from launch, we need to plug in t = 4 into the equation h(t) =[tex]-t^2[/tex] + 19t + 14. This gives us h(4) =[tex]-4^2[/tex] + 19(4) + 14 = -16 + 76 + 14 = 68 feet. Therefore, the height of the firecracker after 4 seconds from launch is 68 feet.
To find the height of the firecracker after 4 seconds from launch, we need to use the equation h(t) =[tex]-t^2[/tex] + 19t + 14. This equation models the path of the firecracker, with h(t) being the height in feet of the firecracker at any given time, t. When we plug in t = 4, we get h(4) = [tex]-4^2[/tex] + 19(4) + 14 = -16 + 76 + 14 = 68 feet. So, the height of the firecracker 4 seconds after launch is 68 feet. This equation allows us to calculate the height of the firecracker at any given time, making it a useful tool for predicting the trajectory of the firecracker.
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Is How far from work does Jeremy live? a statistical question
a) The question "How far are we from the restaurant?" is not statistical question
b) The question "How long will it be until we get there?" is the statistical question.
Now let's take a look at the two questions mentioned above and determine whether or not they are statistical questions.
The first question, "How far are we from the restaurant?" is not a statistical question. This is because the answer to the question does not involve any data or analysis. It is a simple question that can be answered with a measurement, such as the distance in miles or kilometers.
On the other hand, the second question, "How long will it be until we get there?" can be considered a statistical question. This is because the answer to the question depends on various factors that can be analyzed statistically, such as the distance to the restaurant, the speed of the vehicle, the traffic conditions, etc.
In conclusion, statistical questions are those that can be answered through the collection and analysis of data. The two questions mentioned above illustrate the difference between a simple measurement question and a statistical estimation question.
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Complete Question:
Last night, Jeremy and his family went out for dinner. The questions below came up on their way to the restaurant or during the meal. Decide whether or not each question is a statistical question, and justify your decision.
How far are we from the restaurant?
How long will it be until we get there?
What two criteria must a graph meet to show a proportional relationship?
Answer:
Two variables are proportional if they can be written as y=kx y = k x , where k is the constant of proportionality. If y and x are proportional, then for any pair of x and y , the ratio yx=k y x = k should be the same.
Step-by-step explanation:
Write an explicit formula for an, the nth term of the sequence 23, 19, 15, ....
Answer:
[tex]a_{n}[/tex] = - 4n + 27
Step-by-step explanation:
there is a common difference between consecutive terms, that is
19 - 23 = 15 - 19 = - 4
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 23 and d = - 4 , then
[tex]a_{n}[/tex] = 23 - 4(n - 1) = 23 - 4n + 4 = - 4n + 27 or 27 - 4n
Answer the questions with blue
AnswerAnswer:
1. no
2. no
4. no
6. yes, none of the numbers repeat
8. yes, none of the numbers repeat
Step-by-step explanation:
It has been a while since I did this so not exaI'm not exactly sure about the rest of them.
what are the possible rational roots of f(r)=2r^3-2r^2+r+8
Answer:
The possible rational roots of f(r) can be found using the Rational Root Theorem, which states that any rational root of the polynomial equation with integer coefficients must have the form p/q, where p is a factor of the constant term (in this case, 8) and q is a factor of the leading coefficient (in this case, 2).
Therefore, the possible rational roots of f(r) are: ±1, ±2, ±4, ±8, ±1/2, ±1/4
Step-by-step explanation:
a bag of 16 balls contains one red, three yellow, five green, and seven blue balls. suppose four balls are picked, sampling with replacement. (a) find the probability that the sample contains at least two green balls. (b) find the probability that each of the balls in the sample is a different color. (c) repeat these two problems for the case when the sampling is without replacement.
Sampling with replacement-
a) The probability that the sample contains at least two green balls is 0.4139
b) The probability that each of the balls in the sample is a different color is 0.0577.
c) Sampling without replacement
0.26580.4615a. Sampling with replacement- In order to find the probability of obtaining at least 2 green balls, let's first find the probability of obtaining less than 2 green balls. The probability of obtaining exactly one green ball is:
P(1G) = (5/16) × (11/16)³
The probability of obtaining 0 green balls is:
P(0G) = (11/16)⁴
So, the probability of obtaining at least 2 green balls is:
P(at least 2G) = 1 - P(0G) - P(1G)
⇒ 1 - (11/16)⁴ - (5/16) × (11/16)³
⇒ 0.4139
b. Sampling with replacement- The total number of ways to pick 4 balls from 16 is:
C(16, 4) = 1820
The number of ways to pick 4 balls of different colors is:
C(7, 1) × C(5, 1) × C(3, 1) × C(1, 1) ⇒ 105
So, the probability of picking 4 balls of different colors is:
P(all different) = 105/1820
⇒ 0.0577
c. Sampling without replacement-
In this case, the probability of obtaining less than 2 green balls is:P(1G) = (5/16) × (11/15) × (10/14) × (9/13) + (11/16) × (5/15) × (10/14) × (9/13) + (11/16) × (10/15) × (5/14) × (9/13) + (11/16) × (10/15) × (9/14) × (5/13)
⇒0.4645
The probability of obtaining 0 green balls is:
P(0G) = (11/16) × (10/15) × (9/14) × (8/13)
⇒ 0.2697
So, the probability of obtaining at least 2 green balls is:
P(at least 2G) = 1 - P(0G) - P(1G) = 1 - 0.2697 - 0.4645
⇒ 0.2658
The total number of ways to pick 4 balls from 16 is:C(16, 4) = 1820
The number of ways to pick 4 balls of different colors is:
C(7, 1) × C(5, 1) × C(3, 1) × C(1, 1) = 105
To pick 4 balls of different colors, there are C(4, 1) ways to choose which color the 4 balls will have. For each choice of color, there are 4! ways to pick 4 balls of that color.
Thus, the total number of ways to pick 4 balls of different colors is:
C(4, 1) × 4! × C(7, 1) × C(5, 1) × C(3, 1) × C(1, 1)
⇒ 840
So, the probability of picking 4 balls of different colors is:
P(all different) = 840/1820
⇒ 0.4615
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15. Barney likes 27 but not 25; he likes 216 but not 220; he likes 343 but not 345. Which does he like:
Hence according to the given pattern next number will be 1000.
A cube is a solid three-dimensional shape with six square faces, eight vertices, and twelve edges that is used in mathematics or geometry. Also said to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent real-world example and is useful for boosting cognitive function. Similar to this, there are several examples in everyday life, such as six-sided dice, etc. Three-dimensional structures and figures with surface areas and volumes are the focus of solid geometry.
The pattern or sequence in the provided series of numbers is known as the number pattern. The common relationship between the provided collection of numbers is revealed by the number pattern. A number pattern is a regular pattern of numbers that repeats itself.
3x3x3= 27
6x6x6= 216
7x7x7= 343
10x10x10= 1000
Hence The complete question is-
Barney likes 27 but not 25; he likes 216 but not 220; he likes 343 but not 345. Which does he like: 16, 81, 127, 1000, or 1021?
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Add 450 to 348, and then multiply by 7. 450 + 348 × 7
(450 + 348) × 7
450 × 7 + 348
450 × (7 + 348)
The correct expression for the mathematical statement "Add 450 to 348, and then multiply by 7." is (450 + 348) × 7 , the correct option is (b).
An Algebraic Expression is defined as a mathematical phrase which contains one or more variables, numbers, and are joined by mathematical operators such as addition, subtraction, multiplication, and division.
The expression for the mathematical statement "Add 450 to 348, and then multiply by 7" is represented in ,option (b) (450 + 348) × 7 ;
Let the statement be read in two parts,
First "Add 450 to 348", which means we add 450 and 348 together, which is represented as "450+348";
In second part ,we "Multiply by 7", which means we multiply result in first part by 7.
Putting it all together, we get:
⇒ (450 + 348) × 7
Therefore , the correct Algebraic Expression is (b) (450 + 348) × 7.
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The given question is incomplete, the complete question is
Select the correct expression for the given mathematical statement. "Add 450 to 348, and then multiply by 7."
(a) 450 + 348 × 7
(b) (450 + 348) × 7
(c) 450 × 7 + 348
(d) 450 × (7 + 348)
Simplifying positive expressions in multiplication.
Simplify.
(3y)4
Write your answer without parentheses.
Answer:
[tex]81y^4[/tex]
Step-by-step explanation:
You can start by separating the inside terms:
[tex](3y)^4 = (3)^4(y)^4[/tex]
Then notice
[tex]3^4=3*3*3*3=81[/tex]
So
[tex](3)^4(y)^4=81 y^4[/tex]
i need help asap please
Answer:
no question is there for me to answer
Step-by-step explanation:
(6×100+33)/100
=633/100
=6.33
The guitar francisca wants is on sale at two different stores. The original price of the guitar at both stores is $160. At which store is the guitar less expensive? How much less expensive? A. Store a offers 75% B.Store B offers 50% off + additional 30% off in all discounted prices. Its two questions so please answer correctly.
Using the given information, the guitar is less expensive at Store A
It is less expensive by $16
Determining the store which the guitar is less expensiveFrom the question, we are to determine where the guitar is less expensive.
A. Store A offers a discount of 75%. Therefore, the price of the guitar at Store A after the discount is:
Price at Store A = Original price * (1 - Discount percentage)
Price at Store A = $160 * (1 - 0.75)
Price at Store A = $40
Thus, the guitar is $40 at Store A after the discount.
B. Store B offers a discount of 50% off the original price, followed by an additional 30% off in all discounted prices. This means that the price of the guitar at Store B after the two discounts is:
Price at Store B = Original price * (1 - First discount percentage) * (1 - Second discount percentage)
Price at Store B = $160 * (1 - 0.5) * (1 - 0.3)
Price at Store B = $160 * 0.5 * 0.7
Price at Store B = $56
Thus, the guitar is $56 at Store B after the two discounts.
Hence, the guitar is less expensive at Store A
$56 - $40 = $16
It is less expensive by $16
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Please Help
In this unit, you’re factoring a variety of polynomials. But not all polynomials can be factored! Here are some examples: x squared minus 6 x minus 5 x squared plus 4 3 x squared plus 2 x plus 1 x cubed plus 2 x squared plus 2 x plus 3 We might say that these polynomials cannot be factored further, or that they are completely factored. This means the expressions cannot be rewritten as the product of two or more quantities that divide them exactly. In this discussion, you’ll work with your classmates to examine some more examples of this. In your first post, write a polynomial that cannot be factored further. Explain in detail how you know it can’t be factored further. Describe the factoring techniques that might work with this polynomial, and show why they don’t work. Please follow these guidelines for your discussion posts: Write at least 150–300 words. Make sure your posts are grammatically and mechanically correct. Address all parts of the prompt. Provide at least one example to support your response. (Example choices include an anecdote, statistic, and/or textual evidence.)
A rectangular tank is filled with water to a height of 8 centimeters. How much more water is needed to till the tank completely? Give answer in milliliters. (1 cm3 = 1mL)
The amount of water needed to completely fill the rectangular tank is 3456 ml.
Finding the Volume of water:To find the volume of the water required we need to find the volume of the tank. Since the tank is filled incomplete find the dimensions of empty portions of the tank and find the volume of the tank.
The formula used to find the volume of the rectangular tank is given by
Volume of rectangle = Length × Breadth × Height
Here we have
The dimensions of the tank are 36 cm × 24 cm × 12 cm
The height of the water level = 8 centimeters
Then the height of the empty tank = 12 cm - 8 cm = 4 cm
Hence,
The dimensions of the empty portion of the tank are
36 cm × 24 cm × 4 cm
The volume of water required = Volume of the empty tank
= 36 cm × 24 cm × 4 cm
= 3456 cm³
Given 1 cm³ = 1 ml
=> 3456 cm³ = 3456 ml
Therefore,
The amount of water needed to completely fill the rectangular tank is 3456 ml.
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In a sociological survey, one was interested in estimating the percentage who had used cocaine in a population. Questions of this nature are sensitive and therefore the randomized response technique was used. A regular die was used to randomly distribute the questions. Respondents had to stand behind a screen and read the following instructions:
1) Roll the die once and if it shows 1 or 2 answer the question.
" Have you used cocaine at any time in the past year? "
2) If the die shows 3, 4, 5 or 6 answer the question.
"Does the die show an even number of dots?"
840 people took part in the survey and 314 yes and 526 no were received. Estimate the proportion who have used cocaine in the past year.
Answer with a proportion ie a number between 0 and 1. Use 4 correct decimal places.
0.1667
In a sociological survey, one was interested in estimating the percentage who had used cocaine in a population. Questions of this nature are sensitive and therefore the randomized response technique was used. A regular die was used to randomly distribute the questions. Respondents had to stand behind a screen and read the following instructions:1) Roll the die once and if it shows 1 or 2 answer the question. "Have you used cocaine at any time in the past year?"2) If the die shows 3, 4, 5, or 6 answer the question. "Does the die show an even number of dots?"Estimate the proportion who have used cocaine in the past year.Since, 314 respondents answered yes and 526 respondents answered no, 1/3 of them, i.e., 280 people had answered "Yes" to the cocaine question. Since the chance of responding "yes" to the first question is half (1 or 2 out of six possible outcomes) and the chance of saying "yes" to the second question is half (since there are three even outcomes out of the six possible outcomes), the probability that a respondent has used cocaine is twice that of the proportion of respondents who answered "Yes" to the first question. Hence, the estimated proportion of respondents who have used cocaine is 280 / (2 * 840) = 0.1667, which when rounded to four decimal places, equals 0.1667.Answer:0.1667.
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At a particular university, students' grades in introductory statistic classes are generally unimodal and skewed to the left with a mean of μ=65 and a standard deviation of σ=16. . (Round your answers to four decimal places, if needed.) (a) The distribution of students' grades is (b) If n=39 students are selected at random, the distribution of the sample mean grade is with a mean of and a standard deviation of (c) The probability that the sample mean grade for these 39 students is less than 68. is (d) If n=39students are selected at random, the distribution of the sample total grade with a mean of and a standard deviation of (e) The probability that the total grade for these 39 students is less than 2652.0is
The probability that the total grade for these 39 students is less than 2652.0 is 0.8289.
When answering a question, it is essential to be factually accurate, professional, and friendly. It is also important to be concise and provide step-by-step explanations. Additionally, relevant terms such as "unimodal," "deviation," and "random" should be used where appropriate. HTML formatting should be used where necessary.The solutions to the given problems are:a) The distribution of student's grades is unimodal and skewed left.b) If n=39 students are selected at random, the distribution of the sample mean grade is normal with a mean of μ=65 and a standard deviation of σ=2.5681.c) The probability that the sample mean grade for these 39 students is less than 68 is 0.8461.d) If n=39 students are selected at random, the distribution of the sample total grade is normal with a mean of 2535 and a standard deviation of 30.3848.e) The probability that the total grade for these 39 students is less than 2652.0 is 0.8289.
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can yall help me again im sorry!!!
Answer:
30%
Step-by-step explanation:
156/120 =1.3 =130%-100
How do you write an equation in standard form for a line that passes through (-5, 2) and (1, -2)?
In response to the query, we can state that Hence, 2x + 3y = -4 is the equation equation of the line in standard form.
What is equation?An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
y - y1 = m(x - x1) (x - x1)
where m is the slope of the line and (x1, y1) is one of the line's points.
With the two provided locations, we can first determine the slope of the line:
m = (y2 - y1)/(x2 - x1) = (-2 - 2)/(1 - (-5)) = -4/6 = -2/3
Let's utilise the point-slope form with one of the given points, (-5, 2):
y - 2 = (-2/3)(x - (-5))
y - 2 = (-2/3)x - 10/3
When we multiply both sides by 3, we obtain:
3y - 6 = -2x - 10
2x + 3y = -4
Hence, 2x + 3y = -4 is the equation of the line in standard form.
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How to multiply a exponent with diferent bases
you can multiply the two bases together and then raise the product to the sum of the exponents.
When you have two exponential expressions with different bases and want to multiply them together, you cannot directly multiply the bases together.
An exponent is a mathematical notation that indicates the number of times a number, variable, or expression is multiplied by itself. It is usually written as a superscript to the right of the base number, as in "[tex]a^b[/tex]", where "a" is the base and "b" is the exponent.
The exponent "b" tells us how many times the base "a" should be multiplied by itself. For example, in the expression 2c, the base is 2, and the exponent is 3. This means that we need to multiply 2 by itself three times, resulting in 2 × 2 × 2 = 8.
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Pls help help Algebra1
Answer:
2nd and 5th options
[tex](4x^2-9y^2)(4x^2+9y^2)[/tex]
[tex](4x^2+9y^2)(2x+3y)(2x-3y)[/tex]
Step-by-step explanation:
Notice you can factorize the first term using [tex]a^2-b^2=(a+b)(a-b)[/tex]
so the factors are [tex]a=4x^2 \\[/tex] and [tex]b=9y^2[/tex] since 4^2=16 and 9^2=81
so the first factor form is
[tex](4x^2-9y^2)(4x^2+9y^2)[/tex]
Then you can factor again the first polynomial (the second one cant be factor using real coefficient since terms are strictly positive)
again factors are [tex]a=2x\\[/tex] and [tex]b=3y\\[/tex] so the second factor form is:
[tex](4x^2+9y^2)(2x+3y)(2x-3y)[/tex]
harry invests £8000 in a savings account.
the account pays 2.8% compound interest per year
work out the value of her investment after 4 years
give your answer to the nearest penny
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 8000\\ r=rate\to 2.8\%\to \frac{2.8}{100}\dotfill &0.028\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 8000\left(1+\frac{0.028}{1}\right)^{1\cdot 4}\implies A=8000(1.028)^4 \implies A \approx 8934.34[/tex]
The manufacturers of Caudill automotive oil wish to estimate the mean number of miles that motorists drive between oil changes. A random sample of 54 motorists has a mean of 5900 miles driven between oil changes and a standard deviation of 1350 miles. A 95% confidence interval is found to be (5540,6260) . Which of the following are correct? Select all that apply. a. 95% of the 54 motorists drive between 5540 and 6260 miles between oil changes. b. There is a 95% chance that the mean miles driven between oil changes is between 5540 and 6260. c. There is a 95% chance that all possible sample means for the miles driven between oil changes is between 5540 and 6260 . d. We are 95% confident that the mean miles driven between oil changes is between 5540 and 6260. e. The value 5900 is a parameter. f. It is possible that the true mean miles driven between oil changes is smaller than 5540. g. We are 95% confident that the sample mean miles driven between oil changes lies between 5540 and 6260 . h. Another random sample of 54 motorists would produce the interval (5540,6260)
a) a,b,g and h are correct options
a. 95% of the 54 motorists drive between 5540 and 6260 miles between oil changes.
b. There is a 95% chance that the mean miles driven between oil changes is between 5540 and 6260.
g. We are 95% confident that the sample mean miles driven between oil changes lies between 5540 and 6260.
h. Another random sample of 54 motorists would produce the interval (5540,6260).
The other options are incorrect. The value 5900 is a statistic, not a parameter. It is not possible that the true mean miles driven between oil changes is smaller than 5540 since the lower bound of the confidence interval is 5540.
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After sitting out of a refrigerator for a while, a turkey at room temperature 40 f is placed into an oven. The oven temperature is 72 f. Newton's Law of Heating explains that the temperature of the turkey will increase proportionally to the difference between the temperature of the turkey and the temperature of the oven. The turkey reaches the temperature of 117 f after 1. 5 hours. Using this information, find the value of kk, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the turkey, to the nearest degree, after 4. 5 hours
The value of k is approximately 0.024 and the temperature of the turkey after 4.5 hours in the oven is approximately 53°F.
Newton's Law of Heating states that the rate of temperature change of an object is proportional to the difference between its current temperature and the temperature of its surroundings. We can express this law in terms of the turkey's temperature T(t) as follows:
T'(t) = k(T(t) - 72)
When t = 0, T(0) = 40
When t = 1.5, T(1.5) = 117
Substituting, we get:
(T(1.5) - 72) / (1.5) = k(T(0) - 72)
(117 - 72) / (1.5) = k(40 - 72)
k = (117 - 72) / (1.5 * (40 - 72)) = 0.024
Now, we can use this value of k to determine the temperature of the turkey after 4.5 hours:
When t = 0, T(0) = 40
When t = 4.5, T(4.5) - 72 = (T(0) - 72) * [tex]e^(0.024 * 4.5)[/tex]
T(4.5) - 72 = (40 - 72) * [tex]e^(0.024 * 4.5)[/tex]
T(4.5) - 72 = (-32) * [tex]e^(0.108)[/tex]
T(4.5) = -32 * [tex]e^(0.108)[/tex] + 72
T(4.5) = 53°F
Therefore, the temperature of the turkey after 4.5 hours in the oven is approximately 53°F.
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Use the Intermediate Value Theorem to show that the polynomial P(x) has a real zero in the interval [1,2]. Approximate this zero to two decimal places. P(x)=x5−2x2−12 The approximate zero of P(x) is (Round to two decimal places as needed.) The polynomial is (Type an expression using x as the variable.)
The approximate zero of P(x) is 1.87, and the polynomial is P(x) = x5 − 2x2 − 12.
When finding the real zero in the interval [1,2] using the Intermediate Value Theorem and polynomial P(x) = x5 − 2x2 − 12, there are several steps to follow. We will outline them below. Step 1: State the Intermediate Value Theorem (IVT)The Intermediate Value Theorem (IVT) states that if a function is continuous on an interval [a,b], then it takes on every value between f(a) and f(b) at least once. This means that if f(a) and f(b) have opposite signs, the function has at least one real zero between them. This is useful when the function cannot be solved explicitly. Step 2: Determine the values of f(1) and f(2)Plugging in 1 and 2 to the polynomial P(x) = x5 − 2x2 − 12, we get: f(1) = (1)5 − 2(1)2 − 12 = −13f(2) = (2)5 − 2(2)2 − 12 = 8Hence, f(1) and f(2) have opposite signs, so by the Intermediate Value Theorem, the polynomial P(x) = x5 − 2x2 − 12 has at least one real zero in the interval [1,2]. Step 3: Approximate the real zero to two decimal placesTo approximate the real zero of P(x), we can use a graphing calculator or an iterative method such as Newton's method. Using a graphing calculator, we find that the real zero of P(x) in the interval [1,2] is approximately 1.87 (rounded to two decimal places).Therefore, the approximate zero of P(x) is 1.87, and the polynomial is P(x) = x5 − 2x2 − 12.
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Initial Knowledge Check Solve for u. 4(u+9)=-3(6u-6)+8u Simplify your answer as much as possible
Answer:
pic please so i know some more info thanks
Step-by-step explanation: pic please so i know some more info thanks
I need some help please
The solution to the inequality is [tex]$x\in\left(-\infty,\frac{4}{3}\right]\cup\left[\frac{4}{3},\infty\right)$.[/tex]
What is inequality?
In mathematics, an inequality is a statement that one value or expression is greater than, less than, greater than or equal to, or less than or equal to another value.
The given inequality is
[tex]|\frac{1}{4}x-\frac{1}{3}|\leq \frac{1}{3}[/tex]
To solve the inequality
[tex]$|\frac{1}{4}x-\frac{1}{3}|\leq \frac{1}{3}$,[/tex]
we need to consider two cases:
Case 1:
[tex]\frac{1}{4}x-\frac{1}{3}\geq 0$[/tex],
which gives
[tex]$\frac{1}{4}x\geq\frac{1}{3}$[/tex] or
[tex]$x\geq\frac{4}{3}$.[/tex]
Substituting this value of x in the inequality, we get:
[tex]$$\left|\frac{1}{4}\cdot\frac{4}{3}-\frac{1}{3}\right|\leq\frac{1}{3}$$[/tex]
Simplifying, we get [tex]$\frac{1}{3}\leq\frac{1}{3}$[/tex], which is true.
Case 2: [tex]$\frac{1}{4}x-\frac{1}{3} < 0$[/tex], which gives [tex]$\frac{1}{4}x < \frac{1}{3}$[/tex] or [tex]$x < \frac{4}{3}$[/tex].
Substituting this value of x in the inequality, we get:
[tex]$$\left|\frac{1}{4}\cdot\frac{4}{3}-\frac{1}{3}\right|\leq\frac{1}{3}$$[/tex]
Simplifying, we get [tex]$\frac{1}{3}\leq\frac{1}{3}$[/tex], which is true.
Therefore, the solution to the inequality is [tex]$x\in\left(-\infty,\frac{4}{3}\right]\cup\left[\frac{4}{3},\infty\right)$.[/tex]
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simplify the square root of 5 divided by 75
The square root √(5/75) expression when simplified is 1/15√15
How to simplify the square root expressionGiven the expression:
square root of 5 divided by 75
This is a radical expression
Mathematically, this can be expressed as
√(5/75)
To simplify the square root of 5 divided by 75, we can first simplify the denominator:
75 = 15 x 5
So, the expression becomes:
√(5/75) = √(5/15 * 5)
√(5/75) = √(1/15)
√(5/75) = 1/√15
To simplify further, we can rationalize both the numerator and denominator
So we have
√(5/75) = 1/√15 * √15/√15
Evaluate
√(5/75) = 1/15√15
Therefore, the simplified expression is 1/15√15
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Find the interest due to the bank on a loan of $1,000 at 7.5% for 280 days.
Answer: $57.53
Step-by-step explanation:
for a tetrahedron abcd a plane p is called a middle plane if all four distances from the vertices a, b, c and d to the plane p are the same. how many middle planes are there for a given tetrahedron?
There are no middle planes for a given tetrahedron. This is because a tetrahedron is a three-dimensional figure with four faces, each of which is a triangle. Each of the four vertices of a tetrahedron is equidistant from one of the faces, but not from any of the other three faces. Therefore, there are no planes that are equidistant from all four vertices of a tetrahedron.
To further explain, let's consider the four distances from the vertices A, B, C, and D to a plane P. If all four distances are the same, then the plane P must be equidistant from all four vertices. However, this is not possible in a tetrahedron because each vertex is closer to one face than it is to the other three faces. Therefore, there are no middle planes in a tetrahedron.
In conclusion, there are no middle planes for a given tetrahedron because each vertex is closer to one face than it is to the other three faces.
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Daniel has $25 to spend at the fair. The admission to the fair is $4, and the rides cost $1.50 each. Daniel rides x rides at the fair. What inequality represents this situation?
*
5 points
Option 1 4+1.50r<25
Option 2 4+1.50r>25
Option 3 4r+1.50>25
Option 4 4r+1.50<25
Answer:
option 1 4+1.50r<25 is the answer
Subtract: (13z^(9)+6v)-11z^(9) ur answer should be in simplest terms. Enter the correct answer.
Answer:
[tex]2z^9+6v[/tex]
Step-by-step explanation:
Combine like terms.
[tex]13z^9 + 6v - 11z^9 \\13z^9-11z^9 + 6v\\2z^9+6v[/tex]