The given statement "If Dante obtains a part-time job, he can afford a car payment" is valid.
What are statements and conclusions?Logical reasoning essentially consists of a statement and a conclusion. In this part, a claim and several inferences will be made. It is necessary to select the statement's logically following conclusion.
Given that If Dante obtains a part-time job, he can afford a car payment. Dante can afford a car payment.
Conclusion: Dante obtained a part-time job.
From the given statement it is concluded that Dante obtained a part-time job which means that he is financially stable now to pay for the car.
Therefore, the given statement "If Dante obtains a part-time job, he can afford a car payment" is valid.
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The temperature on Wednesday at 5:00 p.m. was 15°F. In the following 12 hours, the temperature dropped 22°F. The temperature on Thursday at 5:00 p.m. was 27°F.
Part A: What was the temperature on Thursday at 5:00 a.m.? Explain or show how you got your answer.
The temperature on Thursday at 5:00 a.m. was
The temperature required on Thursday at 5:00 a.m. was observed as -7°F
given,
The temperature on Wednesday at 5:00 p.m. = 15°F
the temperature dropped 22°F in the following 12hours
The temperature on Thursday at 5:00 p.m. was 27°F.
the temperature on Thursday at 5:00 a.m. is calculated with a vertical number line.
number line - A number line is defined as the number marked on the line calibrated into an equal number of units.
For example -1, 0, 1, and so on.
Thus, the temperature on Thursday at 5:00 a.m. is
=15° - 22°
= -7°
The temperature required on Thursday at 5:00 a.m. was observed as -7°F
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If alpha and beta are the roots of 3x²-4x+1. Find
a) alpha²-beta²
b) 2/alpha²+2/beta²
c)2/alpha²-2/beta²
From Vieta's formulas, we have
[tex]3x^2 - 4x + 1 = 3 (x - \alpha) (x - \beta) \\\\ ~~~~~~~~~~~~~~~~~ = 3x^2 - 3 (\alpha + \beta) + 3\alpha\beta \\\\ \implies \begin{cases} \boxed{\alpha + \beta = \frac43} \\\\ \boxed{\alpha\beta = \frac13} \end{cases}[/tex]
a) Note that
[tex](\alpha + \beta)^2 = \alpha^2 + 2\alpha\beta + \beta^2 \\\\ \implies \alpha^2 - \beta^2 = (\alpha+\beta)^2 - 2\alpha\beta - 2\beta^2[/tex]
We have exact values for [tex]\alpha+\beta[/tex] and [tex]2\alpha\beta[/tex], but sadly not for [tex]-2\beta^2[/tex]. This means we'll need to solve for [tex]\beta[/tex] explicitly.
By factorizing, we have
[tex]3x^2 - 4x + 1 = (3x - 1) (x - 1) = 0 \\\\ \implies x = \dfrac13 \text{ or } x = 1[/tex]
Then the value of [tex]\alpha^2-\beta^2[/tex] depends on which is chosen to be the larger root, and
[tex]\alpha^2 - \beta^2 = \dfrac1{3^2} - 1^2 = \boxed{-\dfrac89} \text{ or } \alpha^2 - \beta^2 = 1^2 - \dfrac1{3^2} = \boxed{\dfrac89}[/tex]
While we're at it, we can also immediately find
[tex]\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta = \left(\dfrac43\right)^2 - 2\cdot\dfrac13 = \dfrac{10}9[/tex]
b) Combine fractions to get
[tex]\dfrac2{\alpha^2} + \dfrac2{\beta^2} = \dfrac{2\beta^2 + 2\alpha^2}{\alpha^2\beta^2} \\\\ ~~~~~~~~~~~~~ = 2 \cdot \dfrac{\alpha^2 + \beta^2}{(\alpha\beta)^2} \\\\ ~~~~~~~~~~~~~ = 2\cdot \dfrac{\frac{10}9}{\left(\frac13\right)^2} \\\\ ~~~~~~~~~~~~~ = \boxed{20}[/tex]
c) Combine fractions again.
[tex]\dfrac2{\alpha^2} - \dfrac2{\beta^2} = 2 \cdot \dfrac{\beta^2 - \alpha^2}{(\alpha\beta)^2} \\\\ ~~~~~~~~~~~~~ = -2\cdot \dfrac{\pm\frac89}{\left(\frac13\right)^2} \\\\ ~~~~~~~~~~~~~ = \boxed{\pm16}[/tex]
Reduce the following notes and determine error of closure bs hi fs elevation remarks 2.25 1149.92 bm start 3.58 5.99 12.56 4.66 5.68 10.66 4.55 9.88 10.15 2.33 1.02 1.66 4.59 bm start
The error in the closure is equal to the difference in the actual value of evaluation and the measured value of evaluation of the same point which is equal to 0.02 units.
What do you mean by the term error of closure?There is a discrepancy between the existing coordinates and the computed coordinates. The amount by which a quantity obtained by a series of related measurements differs from the true or fixed value of the same quantity sometimes known as a closure mistake. The difference between the real value of a series of angles and its exact value in theory. likewise known as an angular mistake of closure. The degree to which two azimuth readings for a line that were obtained through distinct surveys or along different routes do not perfectly match one another. is also known as an azimuth closure error.
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The base of a solid right pyramid is a square with an edge length of n units. The height of the pyramid is n − 1 units.
The correct option is C. One-third n²(n − 1) units³ = ⅓ n²(n-1) units³; volume of the pyramid.
What is referred as the solid right pyramid?A right pyramid is one that has the upper end straight just above centroid of a base. A regular pyramid is thus a subset of a right pyramid.
As, per the given question;
Edge Length = n units
Height of the pyramid = n - 1 units
The formula for volume of a solid right pyramid is;
Volume = ⅓Ah
Where, A is the area of the base.
h is the height of the pyramid
Since, pyramid has the square base;
Calculate the area;
Area, A = edge × edge
A = n × n
A = n²
Put the value of area in volume;
Volume = ⅓Ah
Substitute n² at A and n - 1 at h.
Solve the expression;
Volume = ⅓ × n² × (n - 1)
Volume = ⅓n²(n-1).
Therefore, the volume of the solid right pyramid is calculated as V = ⅓n²(n-1) units³.
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The complete question is -
A solid right pyramid has a square base with an edge length of n units. The height of the pyramid is n minus 1 units.
Which expression represents the volume of the pyramid?
A. One-third n(n − 1) units³
B. One-third n²(n − 1)² units³
C. One-third n²(n − 1) units³
D. One-third n³(n − 1) units³
As the sample size increases, the margin of error _____. a. decreases b. increases c. stays the same d. becomes negative
As the sample size increases, the margin of error a. decreases
What is a margin of error?In a random survey sample, the margin of error is a statistical measure that takes into account the discrepancy between actual and anticipated findings. Simply said, you may determine the degree of unpredictability in data and research results using the margin of error.
The number of distinct samples that are measured or observations that are used in a survey or experiment is known as the sample size. For instance, your sample size is 100 if you examine 100 samples of soil for signs of acid rain. If 30,500 completed questionnaires from an online survey were returned, your sample size is 30,500.
Hence, as the sample size increases, the margin of error decreases.
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12-(8+1)^2
explain please
Answer:
steps
12-(8+1)^2
=12-9^2
12-81
=-69
Step-by-step explanation:
A school field trip cost $1,144 for a class of 22 students. What is the cost for each student?
for 1983 through 1989, the per capita consumption of chicken in the u.s. increased at a rate that was approximately linear. in 1983, the per capita consumption was 33.3 pounds, and in 1989 it was 48 pounds. write a linear model for per capita consumption of chicken in the u.s. let t
In 1995, we would anticipate a per capita consumption of 54.3 pounds of chicken.
What is per capita consumption?Per capita consumption is the yearly use of services and goods by each individual, calculated by dividing the total population's use of goods and services. This variable measures personal economic well-being directly.So,
According to the data, per capita consumption was 39.7 pounds in 1983 and 47 pounds in 1989.Per capita consumption is the yearly use of services and goods by each individual, calculated by dividing the total population's use of goods and services. This variable measures personal economic well-being directly.Assume t=0 corresponds to the year 1980.As a result, we can express the given data as ordered pairs (3,39.7) and (9,47).We can compute a linear function that passes through these points.Let us first calculate the slope of the linear function:
[tex]m=\frac{y_2-y_1}{t_2-t_1}=\frac{47-39.7}{9-3}=\frac{7.3}{6}=\frac{73}{60}[/tex]The required linear function can be written as:
[tex]y-39.7=\frac{73}{60}(t-3)[/tex]When we simplify this, we get:
[tex]y=\frac{73}{60} t+\frac{721}{20}[/tex]To calculate per capita consumption in 1995, enter t=15 into this function.
[tex]y=\frac{73}{60}(15)+\frac{721}{20}=54.3[/tex]Therefore, in 1995, we would anticipate a per capita consumption of 54.3 pounds of chicken.
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The correct question is given below:
For 1983 through 1989, the per capita consumption of chicken in the u.S. Increased at a rate that was approximately linear. In 1983, the per capita consumption was 39.7 pounds, and in 1989 it was 47 pounds. Write a linear model for per capita consumption of chicken in the u.S. Let t represent time in years, where t = 3 represents 1983. Let y represent chicken consumption in pounds. What would you expect the per capita consumption of chicken to be in 1995? What would you expect the per capita consumption of chicken to be in 1995?
Tom needs to drive a total of 13 miles. So far, he has driven 7.3 miles. How many more miles must Tom drive?
Answer:5.7 more miles that Tom has to drive
Step-by-step explanation: you add a extra zero to the 13 which would look like 13.0 and then put the 7.3 under 13.0 and it would look like this
13.0
7.3 and you subtract like normal
Hi i need help with my work
The equation to express the relationship will be y = 5.05 + 2.45x.
How to illustrate the information?Worth of the card = $5.06
It should be noted that the card increases by $2.45.
Therefore, the equation to express the relationship will be:
y = 5.06 + (2.45 × x)
where x = number of years.
y = value of the card.
y = 5.05 + 2.45x
In conclusion, the equation to express the relationship will be y = 5.05 + 2.45x.
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Multiply.
(−5 5/8)⋅(−2 1/3)
9/2 I think
I hope that helped!
Answer:
13.125 or 105/8 or 13 1/8
Step-by-step explanation:
If m/CDE is a straight angle, DE bisects m/GDH, mZGDE = (8x-1), m/EDH = (6x +
m/CDF = 43°, find each measure.
x =
m/GDH=
mZFDH=
m/FDE =
Answer:
From the way the problem is worded:
CDE is a straight angle made up of three angles: CDF of measure 43, FDG of unknown measure and GDE of measure 8x + 1.
EDH is outside CDE and is of measure 6x + 15.
Since DE bisects GDH to form GDE and EDH, those latter two angles are equal and thus 8x + 1 = 6x + 15 and x = 7 and substituting 7 for x, both angles are equal to 57 degrees.
Since CDF is 43 and GDE is 57 and CDE is 180 in total, then FDG = 180 - 43 - 57 = 80 degrees.
Find the value of x so that the line through the pair of points has the given slope.
Points: (x,4) and (5,10)
Slope: 3
What does x =?
Which table represents a linear function?
Answer:
Option C.
Step-by-step explanation:
For a table to be linear, the table must have a constant and even rate of change, meaning as X, the input, increases by 1, Y, the output, increases evenly by a random number we're gonna name "a". Now, a, in this case, is -8. The numbers increase evenly by -8(a), which would classify that function as linear. Thus, option C. is the correct answer.
Find the distance between (0, -8) and (3, -2). Express your answer as a simplified radical, if possible.
O 5√3
O22.5
O √45
O 3√5
Answer:
3√5
Step-by-step explanation:
You use the Distance Formula to solve this.
d=√(x2-x1)^2 + (y2-y1)^2
Plug in your points.
d=√(3-0)^2 + (-2- -8)^2
Subtract and square.
d=√9 + 36
Add
d=√45
The square root of 45 is 6.70, so you would look for radicals.
3√5 is 45. <3
A cold drink initially at 35 f warms up to 42 f in min while sitting in a room of temperature 72f. how warm will the drink be if left out for 30 min?
[tex]$$\begin{aligned}&T^{\prime}=-k(T-72) \quad T(0)=35 \text { (given) } \\&\frac{d T}{T-72}=-k d t-\left\{q^n(1)\right. \\&\text { Solphy } k g^n(1) \\&\ln (T-72)=0-k t+1 \\&T-72=e^{-k t+t} \\&T-72=e^{-k t} e^l \\&\text { let } e^r=C \\&T-72=C e^{-k t} \\&T=72+C e^{-k t} \\&T(t)=72+c e^{-k t}(2)\end{aligned}$$[/tex][tex]$T(t)=72+c e$ Now at $t=Q \mathrm{~mm} \quad T=42$ given Now at $t=Q \min T=$$$\begin{aligned}&\text { yed: } 72+4 e^{-k t} \\&35=72+c e^{-k 0} \\&C=-37 \\&\text { at }+=2 \text { min } T=42 \\&\text { a gaim puting in \&qn } \\&42=72-3+e^{-2 k}\end{aligned}$$[/tex][tex]$$\begin{array}{rl}-\frac{30}{37} & =e^{-2 k} \\e^{-2 k} & =\frac{30}{37} \\-2 k & =\ln \left(\frac{30}{37}\right) \\k & =0.1048 \\p 1 h y & m n \\T(t) & =72-37 e^{-0.1048+} \\T(15) & =72-37 e^{-0.1048 \times 15} \\T(15) & =72-37 \times 1 \\T(15) & =64.31 \\& =\end{array}$$[/tex]
What is Fahrenheit?The unit is the degree Fahrenheit, represented by the sign °F. There are various accounts of how he initially defined his scale, but the initial paper suggests that the lower defining point, 0 °F, was established as the freezing temperature of a brine solution made from a combination of water, ice, and ammonium chloride (a salt). The other limit established was his best estimate of the average human body temperature, originally set at 90 °F, then 96 °F (about 2.6 °F less than the modern value due to He did, however, mention a midpoint at 32 °F, which would be the temperature of ice water.
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One packet of hot cocoa weighs 1.38 ounces. How much will 8 packets weigh?
Answer:
Your answer will be 11.04
Step-by-step explanation:
1.38 × 8= 11.04
The options are
A. (6, 3)
B. (1, -4)
C. (2, 1)
D. (0, 3)
Answer:
Correct answer is D.
Step-by-step explanation:
A. 6 = 3-3 ×
B. 1 = -4-3 ×
C. 2 = 1-3 ×
D. 0 = 3-3 ✓
What is the most specific name for the figure? I NEED THE ANSWER
The most specific name for the figure in the image is a Rectangle. Option B
This is further explained below.
What is the most specific name for the figure?Generally, According to the principles of Euclidean geometry, a Rectangle is considered to be a regular quadrilateral since it has four sides of equal length amongst opp two sides
Another way to describe it is as a rectangle with two neighboring sides that have the same length.
The term coordinate is pronounced exactly the same as o-ordinate. When used as an adjective, these phrases might signify to have the same status or rank, to have something to do with coordination, or to have something to do with an intersection of indices.
In conclusion, A Rectangle is the most accurate description of the shape that can be seen in the picture. Alternative B
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The cost of a school dance is given by the formula: c = 2p + 500 where c represents the total cost in dollars, and p the number of students attended. How many students can attend the school dance if we have $1,672 to spend on the dance?
Answer:
586 students can attend the school dance if we have $1,672 to spend on the dance.
Step-by-step explanation:
1672 = 2p + 500 Subtract 500 from both sides of the equation
1172 = 2p Divide both sides of the equation by 2
586 = p
hte number of left handed people in the world is one-tenth the number of right handed people. the percent of right-handed people
The percentage of right-handed people is 1%.
What do you mean by the term percent?Percent signifies out of one hundred. It is frequently represented by the symbol "%," even when there aren't 100 entries. After that, the figure is scaled so that it can be put in comparison with 100. Additionally, changes in numerical quantities are denoted by percentages.
We have a bowl of fruit, for instance, with three apples and one orange. Three out of four, or 3/4, or 75 out of 100, or 75 percent, are apples.
A ratio can also be expressed as a fraction or decimal in addition to being written as a percentage. There are methods for converting decimals or fractions to percentages.
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ASAP GIVING BRAINLYIEST
Which of the following is true?
|−4| < 3
|−4| < |3|
|−3| < −4
|−3| < |−4|
Step-by-step explanation:
- 4.3 its the same as (-4.3)
what Is the expanded notation for 8013
Answer:
8.013 x 10^3
Step-by-step explanation:
question one-half cup of black beans provides 15% of the potassium you need daily. you must get the remaining 2890 milligrams from other sources. how many milligrams of potassium should you consume daily? question one-half cup of black beans provides 15% of the potassium you need daily. you must get the remaining 2890 milligrams from other sources. how many milligrams of potassium should you consume daily?
The amount of potassium you should consume daily is 510 miligrams if 15 percent of potassium you daily need.
Let the total amount of sources of nutrient you consumed daily be x miligrams.
According to the given question.
One-half cup of black beans provides 15 percent of the potassium.
Also, you get remaning nutrients from 2890 miligrams of other sources.
⇒ you get 85 percent of remaining nutrients from other sources.
So, we can say that
85 percent of x = 2890 miligrams
⇒ 85/100 × x = 2890 miligrams
⇒ x = (2890 × 100)/85
⇒ x = 3400
So, the total amount of source of nutrients is 3400.
Therefore,
The amount of potassium you should consume daily
= 15 percent of 3400
= (15/100) × 3400
= 15 × 34
= 510 miligrams
The amount of potassium you should consume daily is 510 miligrams if 15 percent of potassium you daily need.
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Is the following statement true or false?
3 is not a character of that set. answer is False
What is the absolute value of
x = 8 and x = 18
Answer:
8, 18
Step-by-step explanation:
The absolute value is the distance of the point from 0. In this question, it would be the number itself.
Answer:
The answer would be 8 and 18
Step-by-step explanation:
To solve an equation containing absolute value, isolate the absolute value on one side of the equation. Then set its contents equal to both the positive and negative value of the number on the other side of the equation and solve both equations. Solve | x | + 2 = 5. Isolate the absolute value.
4(18g-12)=12(6g-4)+4
Help me solve this please
Answer:
No solution.
Step-by-step explanation:
4(18g - 12) = 12(6g -4) + 4
4(18g) - 4(-12) = 12(6g) - 12(-4) + 4
72g + 48 = 72g + 48 + 4
72g + 48 = 72g + 52
72g -72g + 48 = 72g -72g + 52
48 = 52 This is a false solution so there is no solution. No value for x will make this equation true.
The sumerian mathematical system was based on units of sixty, ten, and six and survives in what modern system?
The sumerian mathematical system was based on units of sixty, ten, and six and survives in what modern system time measurement.
What is sumerian mathematical system?
Sumer (a region of Mesopotamia, present-day Iraq) is sometimes referred to as the Cradle of Civilization because it was the origin of writing, the wheel, agriculture, the arch, the plow, irrigation, and many other accomplishments.
We really know more about ancient Sumerian and Babylonian mathematics than we do about early Egyptian mathematics because the Sumerians invented the first known writing system, the pictographic cuneiform script, which uses wedge-shaped symbols engraved on baked clay tablets. In fact, we even have math and geometry problems that seem like school exercises.
The base number 60 was created by adding a "celestial" 6 and a "common" 10 in the Sumerian "sexagesimal" system.
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lol last one before i have to watch another lesson love yall
Hey there!
4a + 1 + a + 3
= 4a + 1 + 1a + 3
COMBINE the LIKE TERMS:
= (4a + 1a) + (1 + 3)
= (4a + a) + (1 + 3)
= 4a + a + 1 + 3
= 5a + 4
Therefore, your answer should be:
5a + 4
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
HELP PROONTOOOOOOOOOOOOOOOOOOOOOOOOOO
Answer:
x - 5 = 65
Step-by-step explanation: