The volume of a rectangular prism if the length is 10ft is 250ft2.
What is a prism?A transparent optical prism is a device intended to refract light and has flat, polished surfaces. Prisms do not have two parallel surfaces; at least one of their surfaces must be slanted. Since a triangular prism with a triangular base and rectangular sides is the traditional geometrical shape of an optical prism, this type is typically meant when the word "prism" is used in everyday speech. Certain optical prism varieties don't actually have geometric prism shapes. Any material that transmits the wavelengths for which it is intended can be used to create prisms. Glass, acrylic, and fluorite are common building blocks.
From description, l = 2h = 2w
Since it has a square base,w=h
V = lwh = 2w•w•w = 2w3
Surface area, A = 2(wl+hl+hw) = 2(2w2+2w2+w2) = 250
5w2=250/2 = 125
w2= 25
V= 2(5)3 = 2(125)= 250 ft2
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In a 5000 m race on a 400 m track, each athlete must run 12 ½ laps. kara runs the race at a constant pace and finishes in 17.5 min, while hannah runs at a faster pace and finishes 15.3 min. in fact, hannah ran fast enough that she passed kara during the race. how many laps had hannah run when she caught and passed kara?
Hannah had run 6 complete laps and is running the 7th lap when she surpasses the athlete Kara.
Who is an athlete?An athlete (sometimes known as a sportsman or sportswoman) is a person who participates in one or more sports that require physical stamina, speed, or strength.
Professional and amateur athletes both exist. The majority of elite athletes have extremely well-developed bodies because to rigorous physical training, stringent exercise, and a tight food regimen.
Isotonic exercisers had a greater mean left ventricular end-diastolic capacity and are less prone to experience depression. Athletes are far more prone than the general public to go to massage parlors and pay for the services of massotherapists and masseurs due to their demanding physical activity. Athletes whose sport favors endurance over strength typically consume less calories than other athletes.
Calculations:
Total length of the race (L) = 5000 m
Time taken by Kara (tk) = 17.9 min = 1074 s
Kara's speed (vk) = L/tk = 5000/1074 m/s
Time taken by Hannah (th) = 15.3 min = 918 s
Hannah's speed (vh) = L/th = 5000/918 m/s
Let the number of laps Hannah had run when she passes Kara be n
Distance travelled by Hannah in this time = n*400 = 400n meters
Time taken by Hannah to run n laps = 400n/(5000/918)=367200n/5000=73.44n
Distance travelled by Kara in this time = (n-1)*400 = 400n - 400 meters
Time taken by Kara to run (n-1) laps = (400n-400)/(5000*1074)=(429600n-429600)/5000=85.92n-85.92
= 85.92n - 85.92 = 73.44n
= 12.48n = 85.92
= n = 6.88
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A truck can be rented from Company A for $130 a day plus $0.30 per mile. Company B charges $70 a day plus $0.60 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
Considering the definition of an equation and the way to solve it, the number of miles in a day at which the rental costs for Company A and Company B are the same is 200.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear.
The members of an equation are each of the expressions that appear on both sides of the equal sign.
The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Number of miles in this caseFirst, you define the variable "m" as the number of miles rented from a truck to a company in a day. You know that:
A truck can be rented from Company A for $130 a day plus $0.30 per mile. Company B charges $70 a day plus $0.60 per mile to rent the same truck.So the price of each company is:
Price of company A=130 + 0.30mPrice of company B=70 + 0.60mIf the rental costs for Company A and Company B are the same, the equation in this case is:
Price of company A= Price of company B
130 + 0.30m= 70 + 0.60m
Solving:
130 - 70= 0.60m - 0.30m
60= 0.30m
60÷0.30= m
200= m
In summary, the number of miles in a day at which the rental costs for Company A and Company B are the same is 200.
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a researcher may claim a causal relationship between variables if one variable influences another. please select the best answer from the choices provided t f
The claim that a researcher may infer a causal link between variables if one effects another is False.
What do you mean when you say that variables have casual relationships?If a change in one variable's level results in a change in the other variable, then there is a causal relationship between the two variables. Keep in mind that correlation does not always imply causation. Two variables may be linked together without one of them directly contributing to the other's observable behavior.
For instance,
the chart below illustrates the relationship between ice cream sales and temperature. Any business can utilize the concept of causality. As is clear from the graph, there is a correlation between warmer weather and increased sales.
A casual relationship between two variables only exists when one of the variables actually causes the other to exist, which does not appear to be the case here. Instead, since a change in one variable affects the other, this scenario can be thought of as a correlated relationship.
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I understand that the question you are looking for is:
a researcher may claim a causal relationship between variables if one variable influences another. please select the best answer from the choices provided.(True/False).
13. Measuring bone density Individuals with low bone
density have a high risk of broken bones (fractures).
Physicians who are concerned about low bone density
(osteoporosis) in patients can refer them for special-
ized testing. Currently, the most common method for
testing bone density is dual-energy X-ray absorptiom-
etry (DEXA). A patient who undergoes a DEXA test
usually gets bone density results in grams per square
centimeter (g/cm²) and in standardized units.
7.
Judy, who is 25 years old, has her bone density
measured using DEXA. Her results indicate a bone
density in the hip of 948 g/cm² and a standardized
score of z = -1.45. In the reference population of
25-year-olet women like Judy, the mean bone density
in the hip is 956 g/cm².6
(b) Use the information provided to calculate the standard
deviation of bone density in the reference population.
Using the normal distribution, the standard deviation of bone density in the reference population is of 5.52 g/cm².
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For this problem, the parameters are given as follows:
[tex]X = 948, z = -1.45, \mu = 956[/tex]
Hence we solve for [tex]\sigma[/tex] to find the z-score as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.45 = \frac{948 - 956}{\sigma}[/tex]
[tex]-1.45\sigma = -8[/tex]
[tex]\sigma = \frac{8}{1.45}[/tex]
[tex]\sigma = 5.52[/tex]
The standard deviation of bone density in the reference population is of 5.52 g/cm².
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Which graph displays the solution to 2 − x < −8?
Answer:
D
Step-by-step explanation:
x>10 is your answer. since theres no less than or greater or equal to c and B are automatically out. x>10 says x is greater then 10 so it is D
Its B, always remember to check if the dot is opened or closed on the line!!
A binomial experiment has 4 trials in which p = 0.35. What is the probability of 1 success?
The formula for calculating the probability of one success under certain conditions is:
x=0.4.
What is probability?"The ratio of the number of favorable outcomes to the total number of outcomes is the standard mathematical definition of probability. Probability is never more than one, and it is never equal to that number."
Generally, the equation for Probability is mathematically given as
Probability [tex]$={ }^n C_r p^r q^{n-r}$[/tex]
According to the question,
Total number of trials n'=4
Number of successes r =1
p=0.35
q=1-0.35
q=0.65
Simply replace the value in order to calculate the appropriate probability.
[tex]\text { Probability } &={ }^4 C_1(0.35)^1(0.65)^{4-1} \\[/tex]
[tex]&=\frac{4 !}{(4-1) ! 1 !} \times \frac{35}{100} \times\left(\frac{65}{100}\right)^3 \\[/tex]
[tex]&=4 \times \frac{35}{100} \times \frac{274625}{1000000} \\[/tex]
=0.384475
=0.4
Hence, the probability of 1 success as per the given condition is equal to 0.384475= 0.4.
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The price of a shirt is marked down from $12.59 to $10.00 what percent is decrease of the shirt
The percentage by which the price of the shirt is decreased is 20%.
What is the percentage?In mathematics, a percentage is a number or ratio expressed as a fraction of 100. The abbreviation "pct.", "pct," and sometimes "pc" is also used. A percentage is a dimensionless number with no unit of measurement.So, the price of a shirt is marked down from $12.50 to $10.00.
Previous price = $12.50New price = $10.00Then,
Change in price = Previous price - New price= $12.50 - $10.00= $2.50Now, the shirt's percentage has decreased:
(Change in price)/(Previous price) ×100
Therefore, the percentage by which the price of the shirt is decreased is 20%.
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3. Maria Whetstone, a heating technician, has a gross weekly income of $502.16. Her earnings to date for this year are $20,086.40. How much is deducted from her paycheck this week for Social Security? How much for Medicare?
Deducted from her paycheck this week for Social Security is $31.13.Medicare is equal to $7.28.
Maria Wehstone, Gross weekly income = 502.16 and annual earnigs till date = 20,086.40
Deduction for this week for social security = 6.20% of 502.16$ = $31.13
Deduction for this week for Medicare = 1.45% of 502.16$ = $7.28
Social security is the safety net that a society offers to people and families to ensure that they have access to health care and to assure financial stability, particularly in circumstances of old age, unemployment, illness, invalidity, work injuries, maternity, or the death of a primary earner.
Based on their career earnings, Social Security replaces a portion of your pre-retirement income. Depending on how much you earn and when you decide to begin receiving benefits, Social Security replaces a different percentage of your pre-retirement income depending on your top 35 years of earnings.
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exercise 5.3.1. recall from exercise 4.4.9 that a function f : a → r is lipschitz on a if there exists an m > 0 such that ∣∣∣∣ f(x) − f(y) x − y ∣∣∣∣ ≤ m for all x ?
If f is differentiable on a closed interval [a,b] and if f' is continuous on the interval [a,b], Then f is Lipschitz on [a,b].
What is a Lipschitz function?
If a neighborhood U of x exists for any x in X such that f restricted to U is Lipschitz continuous, then the function is said to be locally Lipschitz continuous. Alternatively, f is locally Lipschitz if and only if it is Lipschitz continuous on each compact subset of X if X is a locally compact metric space.
Now,
Assume that f can be differentiated and that f' is continuous on [a,b]. Therefore, f' is bounded since [a,b] is compact. In other words, for all x [a,b] there exists M > 0 such that: |f'(x)| ≤ M.The Mean Value Theorem therefore ensures that there exists c between x and y such that: [tex]|\frac{f(x)-f(y)}{x-y}|=|f'(c)|\leq M[/tex], for each x,y ∈[a,b].Given that x and y were chosen at random, we can infer that f is Lipschitz on [a,b] since the inequality: [tex]|\frac{f(x)-f(y)}{x-y}|\leq M[/tex], holds for all x,y ∈ [a,b].Hence, If f is differentiable on a closed interval [a,b] and if f' is continuous on the interval [a,b], Then f is Lipschitz on [a,b].
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Suppose the cost in dollars of producing x model kits is
given by the polynomial 500,000 + 2x and the revenue generated from sales is
given by the polynomial 30x - 0.00005 x^2 . Find a polynomial expression for the
profit from making and selling x model kits. Then evaluate the expression for
x = 300,000.
Answer:
1100000
Step-by-step explanation: If x = 300,000, that means 2x is 2 x 300,000, and that makes the equation 500,000 + ( 2 x 300,00). Please don't judge me, I am only in 7th grade. Thank you.
The polynomial expression for the profit from making and selling x model kits is 28x - 500,000 - 0.00005 x² and the profit is 3400000.
What is a polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
It is given that:
Suppose the cost in dollars of producing x model kits is given by the polynomial 500,000 + 2x and the revenue generated from sales is given by the polynomial 30x - 0.00005 x².
The profit = revenue - cost
The profit = (30x - 0.00005 x²) - (500,000 + 2x)
The profit = 30x - 0.00005 x² - 500,000 - 2x
The profit = 28x - 500,000 - 0.00005 x²
Plug x = 300,000 in the profit expression.
The profit = 3400000
Thus, the polynomial expression for the profit from making and selling x model kits is 28x - 500,000 - 0.00005 x² and the profit is 3400000.
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Mariko has an 80:1 scale drawing of the floor plan of her house. on the floor plan the dimensions of her rectangular living room are 1 and 7/8 inches by 2 and 1/2 inches.
What is the area of her real living room in square feet?
You are solving a measurement problem where the numbers 2.058 × 10^9 and 3.0571 × 10^−4 are divided. How many significant digits should the quotient have?
Based on the numbers being divided, the number of significant digits that the quotient should have is 4 significant digits.
How many significant digits should be seen?The number of significant digits from a quotient where numbers divided each other should be the significant digits in the number with the smaller number of significant digits.
The number with the lower significant digits here is 2.058 × 10^9.
In this number, there are 4 significant digits because 0 is between non zero numbers.
The quotient would therefore have 4 significant digits.
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When part of an original figure matches up with part of a copy. These could be segments points or angles.
When a portion of an original figure corresponds to a portion of a duplicate, we refer to them as corresponding parts. This could be in the form of points, segments, angles, or distances.
What exactly do we mean by "corresponding parts"?Parts that match between two congruent triangles are said to as matching. You can identify the corresponding angles and sides.
How many congruent components are there?Triangles are congruent when all 3 types of corresponding sides are congruent. Two triangles have three sides that are equivalent.
How do you determine which sections of a congruent triangle are corresponding?The equals sign with a squiggly line on top indicates that the items on each side of the equation were congruent. Then, identify the corresponding sides. Corresponding sides are sides that match between two triangles. Congruent triangles will have the same length.
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What is the equation of the line that passes through the point (3,-4) and has a
slope of -5/3?
Answer:
y = -5/3x + 1
Step-by-step explanation:
as the photo saying
Write the equation of the given circle.
center at origin, d=12
a pie-shaped (triangular) lake-front lot has a perimeter of 1300 feet. one side is 100 feet longer than the shortest side, while the third side is 300 feet longer than the shortest side. find the lengths of all three sides.
The lengths of the three sides of the triangular lot are: 100 feet, 200 feet and 400 feet.
What is a triangle and its perimeter?
A triangle is a polygon with three edges and three vertices.
Given:
Perimeter of triangular lot = 1300 feetOne side is 100 longer than the shortestOther is 300 feet longer than the shortest.To find: All the sides of the triangular lot.
FInding:
Let the shortest side of the triangular lot be 'x'.
Then, according to the question, one side of the triangular lot = 100 + x and other = 300 + x
As perimeter of a triangle = sum of all the sides,
=> 1300 = x + 100 + x + 300 + x
=> 1300 - 400 = 3x
=> 900 = 3x
=> 300 = x
Hence, the shortest side = 100 feet, a longer side = 200 feet, the longest side = 400 feet for the given triangular lot.
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erik went to the store and bought 4.8 pounds of chocolate covered almonds and 3.7 pounds of yogurt covered almonds how much did he spend
Answer: svsdvcvsdvsdvsdv
vdsvds
Step-by-step explanation:
ght 4.8 pounds of chocolate covered almonds and 3.7 pounds of yogurt covered almonds how much did he spend
Answer:
43.6
Step-by-step explanation:
30 points for anyone who solves this
Answer: The answer is 2 1/12
Step-by-step explanation:
3. "the product of a number and 5.”
Answer:
x * 5
Step-by-step explanation:
prosucts refer to multiplication
Find the slope of the line
Answer:
-2/3
Step-by-step explanation:
(x1, y1) = (4, 1)
(x2, y2) = (1, 3)
m = (y2 - y1) / (x2 - x1) = (3 - 1) / (1 - 4) = 2 / (-3) = -2/3
Note that we used the point with the bigger x as the "first" point. It does not change the result.
A rectangular garage is 13 yards long and 7 yards wide. It costs $3.00 per square yard to put in a new concrete floor. How much would it cost to put a new concrete floor in the garage?
Answer:
it's B
Step-by-step explanation:
after a long section it is B
|60| ___ |-60|
=
<
>
Answer:
|60| = |-60|
Step-by-step explanation:
Now the value of,
→ |60| = 60
→ |-60| = 60
Then the sign will be,
→ |60| = |-60|
→ 60 = 60
Hence, the sign is (=).
Triangle ABC has its vertices at the following coordinates:
A(-4, 1) B(0, 2) C(-11, 3)
Give the coordinates of the image triangle A'B'C' after a 90° counterclockwise rotation about the origin.
Using translation concepts, the coordinates of the image of the triangle are given as follows:
A'(-1,-4), B'(-2,0), C'(-3, -11).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
The rule for a 90° counterclockwise rotation about the origin is given as follows:
(x,y) -> (-y,x).
Hence the coordinates of the image of the triangle are given as follows:
A': (-4, 1) -> (-1, -4).B': (0, 2) -> (-2,0).C': (-11, 3) -> (-3, -11).More can be learned about translation concepts at https://brainly.com/question/4521517
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Please can you answer this for me, I will mark you as the brainliest
Answer:
Area of the shaded region is 53.47 square yd
A cube is made for 1 million cubic centimeters e What is the length of the side of the cube in centimeters?
The length of the side of the cube is 100 centimeters
How to determine the length
The formula for volume of a cube is expressed as:
Volume, V = a³
Where a is the length of its side
Given that the volume is 1 million cubic centimeters = 1, 000, 000
Substitute the values
1, 000, 000 = a³
Find the cube root of both sides
a = ∛10^6
a = 100 centimeters
Thus, the length of the side of the cube is 100 centimeters
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Tony's Carnival charges $25 to enter the park and $4.50 per ride. Ride Palace charges $18 to enter the park and $5 per ride. How many rides do you need to ride for the cost of each park to be the same?
Answer:
14
Step-by-step explanation:
Let x = number of rides.
Tony's cost: 4.5x + 25
Ride's cost: 5x + 18
Set the prices equal and solve for x.
5x + 18 = 4.5x + 25
Subtract 4.5x from both sides.
0.5x + 18 = 25
Subtract 18 from both sides.
0.5x = 7
Multiply both sides by 2.
x = 14
Answer: 14
List 4.6,2.8 repeating,square root,square root of 17 and the square root of 7 form least to greatest
The numbers from least to greatest are -
square root of 7, 2.8, square root of 7 and 4.6.
What is defined as the ascending order and descending order?Descending pattern is defined as it is when numbers (and other objects) are arranged in descending order from the largest to the smallest numbers.
Ascending is defined like when numbers (or even other items) are positioned in ascending order from the smallest to the largest numbers.
We have the numbers provided as;
4.6, 2.8, square root of 17 and the square root of 7.
Then,
square root of 7
√7 = 2.645, and
square root of 17
√17 = 4.123
Thus, the given series becomes;
4.6, 2.8, 4.123, 2.645.
Now, arranging them according to ascending order (least to greatest).
2.645, 4.123, 2.8 and 4.6.
Therefore, the series becomes; square root of 7, 2.8, square root of 7 and 4.6.
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v = u + at
u = 2 a = -7 t = 0.5
whats v
Answer:
A= 3. 5 u=7 t=0.5
Step-by-step explanation:
It will be 8.75
In the language of functions, all of the following are true except one. Identify the false statement.
The dependent variable (output) is a function of the independent variable (input).
The phrase DEPENDENT VARIABLE means output.
The phrase INDEPENDENT VARIABLE means input
The input is determined by the output
1........answe is 1............
bailey has 40 minutes to exercise.it takes bailey 3 minutes to jog around the track and 5 minutes to stretch. she jogs 6 laps around the track and stretches 2 times what is the experssion for this problem?