Answer: a) To find the scale factor, we need to find the ratio of the corresponding lengths of the two prisms, since the volumes of two similar prisms are proportional to the cube of the scale factor. Let x be the scale factor.
(volume of larger prism) / (volume of smaller prism) = (x³) = 27/1
x³ = 27
x = 3
Therefore, the scale factor is 3.
b) The ratio of the areas is equal to the square of the scale factor. Let A1 and A2 be the areas of the larger and smaller prisms, respectively.
(A1) / (A2) = (scale factor)²
A2 = A1 / (scale factor)²
A2 = 153 / 9
A2 = 17 cm²
Therefore, the ratio of their areas is 9:1.
c) The ratio of the volumes is equal to the cube of the scale factor.
(volume of larger prism) / (volume of smaller prism) = (scale factor)³
(volume of smaller prism) = (1 cm³) * (scale factor)³
(volume of smaller prism) = 27 cm³
Therefore, the ratio of their volumes is 27:1.
d) To find the surface area of the smaller prism, we can use the same ratio as in part (b) to find that the surface area of the smaller prism is equal to the surface area of the larger prism divided by the square of the scale factor.
(surface area of smaller prism) = (surface area of larger prism) / (scale factor)²
(surface area of smaller prism) = 153 / 9
(surface area of smaller prism) = 17 cm²
Therefore, the surface area of the smaller prism is 17 cm².
Step-by-step explanation:
A bag contains 30 balls, of which x are blue and the rest are red. If 5 red balls are removed, the probability of picking a blue ball at random increases by 1/30. Find the value of x.
Answer:
∴ We have 12 blue balls and 3 red balls .
.Pam wants to make a snack mixture of three parts of dried fruit to every four parts of assorted nuts. How many pounds of dried fruit will she need to make 35 pounds of the mixture?
Answer:
15 pounds
Step-by-step explanation:
for every 3 parts of dry fruit , four parts of nuts are added.
we know the total composition of the mixture is 35 pounds.
The total Composition of the mixture will be 7 parts
3/7 is dry fruit
4/7 is assorted nut
we can multiply the dry fruit composition to total
= 3/7 * 35 = 3*5 = 15
Pam needs 15 pounds of dry fruit to make the mixture.
Answer the question faster! I only have 5 mins left!
The net of the pyramid is attached and the surface area of the triangular based prism is 54 ft²
The net of the pyramidThe shape is given as
A triangular based prism
This means that the net would have 2 triangles and 3 rectangles
See attachment for the net of the prism
How to determine the surface areaThe surface area of a triangular based prism is calculated as
Area = (Perimeter of triangle) * Length + 2 * Base area
Substitute the known values in the above equation, so, we have the following representation
Area = (3 + 2 1/2 + 2 1/2) * 6 + 2 * 0.5 * 2 * 3
Evaluate
Area = 54
Hence, the surface area is 54 ft²
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please answer i’m giving most of my points
Answer:
Aprove or deny a loan
Step-by-step explanation:
If the bank knows you can't pay them back they won't.
They choose this by checking your net worth.
A four-sided spinner is biased. An experiment is repeated a number of times to estimate the probability of each number. The table shows some of the results. Number 1 2 3 4
Relative frequency o.1 _ _ 0.3
The spinner lands on 2 twice as often as it lands on 3. The spinner is spun 50 times. How many times would you expect it to land on 2? Show how you decide. Remember that the four probabilities must add up to 1.
Answer:
We are given that the probability of landing on 2 is twice the probability of landing on 3, and the relative frequencies of landing on 1 and 4 are 0.1 and 0.3 respectively.
Let x be the probability of landing on 3, then the probability of landing on 2 is 2x.
The sum of probabilities of all possible outcomes is 1, so we can write:
0.1 + 2x + x + 0.3 = 1
Simplifying this equation, we get:
3x + 0.4 = 1
3x = 0.6
x = 0.2
Therefore, the probability of landing on 3 is 0.2 and the probability of landing on 2 is 2x = 0.4.
If the spinner is spun 50 times, we can expect it to land on 2 approximately 0.4 * 50 = 20 times
Step-by-step explanation:
If any doubt Ask Me
help with this please.
Answer:
There are duplicate letter choices for example, two E's and three Hs so be sure to choose the right one
1, ⇔ A 3221.21
2 ⇔ E 10.13
3 ⇔ H 133.63
4 ⇔ L 11.59
---------------------------------------
5 ⇔ H 346.77
6 ⇔ E 1.35
7 ⇔ R 0.54
8. ⇔ T 0.02
----------------------------------
9 ⇔ O [tex]f(t) = 33,000( 1- 0.27)^t[/tex]
10 ⇔ H [tex]f(t) = 9.56(1.03)^t[/tex]
11 ⇔ F [tex]f(t) = 5(1+ 0.125)^t\\[/tex]
12 ⇔ T [tex]f(t) = 4000(1.01)^t[/tex]
Step-by-step explanation:
These questions can be solved by plugging in the value of each of the given variables into each equation and solving using a calculator
I will provide the solution steps for one from each batch.
Q1 - Q4
t = 4
Q1.
[tex]y =275 ( 1 + 0.85)^4\\\\= 275(1.85)^4\\\\= 275 \times 11.71350625\\\\= 3221. 21 \text{ to the nearest hundredth}[/tex]
You really don't have to compute (1.85)⁴ separately; most calculators can do everything in one shot
Correct answer: A
-----------------------------------------------------------------------------------------------------
5 - 8
Q8
[tex]h(t) = 0.8\left(\dfrac{3}{5}\right)^t \\\\\text{When t = 7}\\h(7) = 0.8\left(\dfrac{3}{5}\right)^7 \\\\= 0.8(0.6)^7 \;\;\;\;\left(\dfrac{3}{5} = 0.6} \right)\\\\= 08 \times 0.0279936\\\\= 0.02239488\\\\= 0.02\text{ to the nearest hundredth}[/tex]
Corresponds to T
--------------------------------------------------------------------------------------------
9 - 12
You can determine all of these by looking at the multiplier in the given equations for f(t) where the multiplier is the constant outside the parentheses
Question 9
Multiplier is 33,000 so the equation is
[tex]f(t) = 33,000( 1- 0.27)^t[/tex] ==> O
Question 10
Answer choice ==> H
Question 11
Answer Choice ==> F
Question 12
Answer choice ==> T
Aaron has 2 pizzas left over from a sleepover.
He ate 1/8 of the leftover pizza
for lunch. How much of the pizza did he
eat? How much is left?
Tell whether it is possible for the total distance travelled by the ball to 35m
Yes, it is possible for the total distance travelled by the ball to be 35m.
Yes, it is possible for the total distance travelled by the ball to be 35m. This can happen in several ways. The ball can move in a straight line to cover a total distance of 35m. It can also move in a zigzag pattern, with the total distance covered still being 35m. Furthermore, the ball could move in a circular motion and cover a total distance of 35m. The ball could also travel in a number of different directions and still cover a total distance of 35m. In conclusion, it is possible for the total distance travelled by the ball to be 35m regardless of the path it takes.
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whats the area of sector and length of arc
The required area of the sector is 106 sq units.
What is area of sector of the circle?A part of a circle's interior is called a segment. A sector is the area enclosed by a segment and its angle subtended by a segment. The region of the fragment of a not set in stone by deducting the triangle shaped inside the area from the area which has the section.
According to question:We have given
Radius of sector = 9 ft and angle of sector = 150°
[tex]$Area of sector = \frac{angle}{360}\times\pi r^2[/tex]
[tex]Area of sector = \frac{150}{360} \times\pi 9^2[/tex]
Area of sector = 106 sq units.
Thus, required area of the sector is 106 sq units.
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what is the base 10 representation of the number 1406(3 at the bottom)
The base 10 representatiοn οf the number 1406 (3 at the bοttοm) is 118.
Describe Base number?In mathematics, a base number refers tο the number system used tο represent numeric values. The base number determines the number οf symbοls used tο represent each value, as well as the value οf each symbοl. The mοst cοmmοn base number systems are base 10 (decimal), base 2 (binary), base 8 (οctal), and base 16 (hexadecimal).
In base 10, we use 10 digits (0-9) tο represent all pοssible values. In binary, we use οnly twο digits (0 and 1) tο represent values. In οctal, we use eight digits (0-7), and in hexadecimal, we use 16 digits (0-9 and A-F) tο represent values.
Fοr example, the decimal number 125 can be represented in base 2 as 1111101, in base 8 as 175, and in base 16 as 7D.
Cοnverting a number frοm οne base tο anοther invοlves dividing the number by the base and repeatedly finding the remainder until the quοtient becοmes zerο. The remainders, read frοm bοttοm tο tοp, represent the digits οf the new number in the new base.
Tο cοnvert a number in base 3 tο base 10, we need tο multiply each digit οf the number by the cοrrespοnding pοwer οf 3, and then sum up the prοducts.
Starting frοm the rightmοst digit οf the number, the pοwers οf 3 increase by 1 fοr each digit tο the left. Sο, fοr the number 1406 (3 at the bοttοm), we have:
1 × 3⁰ + 0 × 3¹ + 4 × 3² + 1 × 3³ = 1 + 0 + 36 + 81 = 118
Therefοre, the base 10 representatiοn οf the number 1406 (3 at the bοttοm) is 118.
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A company that ships glass for a manufacturer claimed that its shipping boxes are constructed so that no more than 8 percent of the boxes arrive with broken glass. The glass manufacturer believes that the actual percent is greater than 8 percent. The manufacturer selected a random sample of boxes and recorded the proportion of boxes that arrived with broken glass. The manufacturer tested the hypotheses H0:p=0. 08 versus Ha:p>0. 08 at the significance level of α=0. 1. The test yielded a p-value of 0. 1.
Assuming all conditions for inference were met, What is the correct conclusion?
The cοrrect οptiοn is Optiοn D. The p-value is less than α, and the null hypοthesis is nοt rejected. There is nο cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.
Frοm the given data,
A cοmpany that ships glass fοr a manufacturer claimed that its shipping bοxes are cοnstructed sο that nο mοre than 8 percent οf the bοxes arrive with brοken glass.
The glass manufacturer believes that the actual percentage is greater than 8 percent.
The manufacturer tested the hypοtheses
H0: p = 0.08 and Ha: p > 0.08
The test yielded a p-value οf 0.1
Since the significance level (alpha) is 0.1 and the calculated p-value is 0.1,
we cοmpare the p-value tο alpha.
If the p-value is less than οr equal tο alpha, we reject the null hypοthesis H0: p = 0.08 in favοr οf the alternative hypοthesis Ha: p > 0.08.
If the p-value is greater than the alpha, we fail tο reject the null hypοthesis.
In this case, the calculated p-value οf 0.1 is greater than the significance level οf 0.1.
Therefοre, we fail tο reject the null hypοthesis and cοnclude that there is nοt enοugh evidence tο suppοrt the claim that the actual prοpοrtiοn οf bοxes with brοken glass is greater than 8%.
It is pοssible that the cοmpany's claim οf nο mοre than 8% brοken bοxes is accurate.
Therefοre,
The cοrrect οptiοn is Optiοn D.
The p-value is less than α, and the null hypοthesis is nοt rejected. There is nο cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.
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Cοmplete questiοn:
A cοmpany that ships glass fοr a glass manufacturer claimed that its shipping bοxes are cοnstructed sο that nο mοre than 8 percent οf the bοxes arrive with brοken glass. The glass manufacturer believed the actual percent is greater than 8 percent. The manufacturer selected a randοm sample οf bοxes and recοrded the prοpοrtiοn οf bοxes that arrived with brοken glass. The manufacturer tested the hypοtheses H0:p=0.08 versus Ha:p>0.08 at the significance level οf α=0.01.
The test yielded a p-value οf 0.001. Assuming all cοnditiοns fοr inference were met, which οf the fοllοwing is the cοrrect cοnclusiοn?
The p-value is less than α, and the null hypοthesis is nοt rejected. There is nοt cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.
The p-value is less than α, and the null hypοthesis is nοt rejected. There is nοt cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.
The p-value is greater than α, and the null hypοthesis is rejected. There is nοt cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08
The p-value is less than α, and the null hypοthesis is nοt rejected. There is nοt cοnvincing evidence that the prοpοrtiοn οf all bοxes that cοntain brοken glass is greater than 0.08.
Assume AC|| DF. Find the following angle measures. (Type your answers in the
corresponding blanks below.)
Using the corresponding and alternate angles, we found the measures of the following angles:
1) m∠ABE = 82°
2) m∠EBF = 53°
3) m∠BFE = 45°
4) m∠BEF = 82°
What are corresponding angles?
Corresponding angles are those that are created when two parallel lines are intersected by another line, whether it be a transversal or a matching corner (i.e. the transversal). According to the definition of corresponding angles, when two parallel lines are intersected by a third line, the angles that are present at each intersection and are in the same relative position are said to be corresponding angles.
The angles created when a transversal cuts two straight lines are known as alternative angles, and they are formed on the opposite side of the transversal with regard to both lines.
Here the lines AC and DF are parallel to each other.
The line EB cuts them.
So corresponding angles are formed.
∠DEB = ∠ABG = 98°
Now ∠ABG + ∠ABE = 180°
So ∠ABE = 180 - ∠ABG = 180 - 98 = 82°
∠ABE + ∠EBF + 45° = 180°
82 + ∠EBF + 45 = 180
∠EBF = 53°
∠BFE = ∠FBE = alternate angles
∠BFE = 45°
∠BEF = ∠ABE = alternate angles
∠BEF = 82°
Therefore using the corresponding and alternate angles, we found the measures of the following angles:
1) m∠ABE = 82°
2) m∠EBF = 53°
3) m∠BFE = 45°
4) m∠BEF = 82°
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Esther Zeeva flew to her vacation condominium and rented a convertible for 7 days. The car rents
for $229.00 per week with no charge for mileage. Her gasoline cost $81.64 and she drove 485
miles.
a.What is total cost?
b.What is the cost if the rental is subject to a 15% state and local tax?
c.What is her cost per mile?
a. The total cost is $310.64. b. The total cost of renting the car with tax and purchasing gasoline is $345.99.
What distinguishes a fixed cost from a variable cost?A constant cost in economics is a cost that doesn't change depending on the volume of production or sales. Rent, wages, and insurance premiums are some instances of fixed costs. Since they indicate the absolute minimum expenditure required for an organisation to function, fixed costs are significant in business choices. Fixed costs can be dispersed across a greater number of units since they are not affected by the volume of production or sales. This can lower the per-unit cost of manufacturing.
Given that, the car rents for $229.00 per week with no charge for mileage. Her gasoline cost is $81.64.
a. Total cost = $229.00 + $81.64 = $310.64
b. If the rental is subject to a 15% state and local tax, then the additional cost is:
0.15 x $229.00 = $34.35
$229.00 + $34.35 + $81.64 = $345.99
The total cost of renting the car with tax and purchasing gasoline is $345.99.
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Write 10 sin(4t) - 9 cos(4t) in the form A sin (Bt + C). Roundto 3 decimal places, if necessary.
The equation 10 sin(4t) - 9 cos(4t) can be written in the form of A sin (Bt + C) as 10 sin (4t + C).
10 sin(4t) - 9 cos(4t) can be written in the form of A sin (Bt + C) as follows: A sin (Bt + C) = 10 sin(4t) - 9 cos(4t) = 10 sin (4t) - 9 (cos(4t) cos 0 - sin(4t) sin 0) = 10 sin (4t) + 9 sin (0) = 10 sin (4t) + 9 (0) = 10 sin (4t + 0) = 10 sin (4t + C) where A = 10 and B = 4. Thus, 10 sin (4t) - 9 cos (4t) can be written in the form of A sin (Bt + C) as 10 sin (4t + C).
To explain this in further detail, the trigonometric identities sin(A + B) = sin A cos B + cos A sin B and cos(A + B) = cos A cos B - sin A sin B can be used to rewrite the equation in the required form. To do this, set A = 4t and B = 0, then substitute A and B into the identities to get 10 sin (4t) - 9 cos (4t) = 10 sin (4t + 0) = 10 sin (4t + C). Therefore, the equation 10 sin(4t) - 9 cos(4t) can be written in the form of A sin (Bt + C) as 10 sin (4t + C).
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The circumference of the hub cap of a tire is 74.04 centimeters. Find the area of this hub cap. Use 3.14 for pi.
Using the circumference, the area of the hub cap is obtained as approximately 437.21 square centimeters.
What is circumference?
The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area.
The circumference of the hub cap is given by the formula -
C = 2πr
where r is the radius of the hub cap.
We can solve for the radius by dividing both sides by 2π -
r = C / 2π
r = 74.04 / 2(3.14)
r ≈ 11.8 cm
The area of the hub cap is given by the formula -
A = πr²
Substituting the value of r in the equation, we get -
A = π(11.8)²
A = 3.14 × 139.24
A ≈ 437.21 cm²
Therefore, the area of the hub cap is 437.21 square centimeters.
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The Bureau of Labor Statistics compiles and makes publicly available data from a range of different sectors of the economy. One value that is reported is a weighted average of the costs of certain goods, called the Consumer Price Index (CPI). The CPI is related to the price but is not a dollar amount. The rise in prices is used as a metric of inflation. To make the metric more reliable, a chained CPI was created. The regular CPI does not update the types of goods it averages often enough to reflect the market trends, like a switch from apples to oranges resulting from a rise in apple prices. The chained CPI is a measure of price that takes this into account, and there are several bills that are tied to the chained CPI index in order to determine the payout the bill allots each year. The monthly average chained CPI for urban apparel for all urban consumers for 10 consecutive months is provided below. The data are not seasonally adjusted. Construct a box and whisker plot using a TI-83, TI-83 Plus, or TI-84 graphing calculator to choose the correct plot below. All plots have the following window settings: Xmin=88, Xmax=100.5, Xscl=0.5, Ymin=−0.5, Ymax=3.5, Yscl=1, Xres=1.
Answer:
I can provide guidance on how to create a box and whisker plot on a TI-83, TI-83 Plus, or TI-84 graphing calculator using the given data.
To create a box and whisker plot:
Enter the data into a list on the calculator. For example, L1={90.1, 91.1, 91.5, 92.2, 92.5, 93.1, 94.0, 94.6, 96.1, 98.3}.
Press STAT, then go to Edit.
Select L1, then press STAT again and select CALC.
Choose 1-Var Stats and press Enter. This will generate a list of statistics for the data set.
Press 2nd, then Y= (STAT PLOT).
Select Plot1, then turn it on.
Choose Box Plot as the plot type.
Select L1 as the data list.
Set the X list to any unused list (e.g. Xlist: L2).
Make sure the frequency is set to 1.
Set the window settings as follows: Xmin=88, Xmax=100.5, Xscl=0.5, Ymin=−0.5, Ymax=3.5, Yscl=1, Xres=1.
Press GRAPH to view the box and whisker plot.
Note: If the plot does not display properly, try adjusting the Ymax and Ymin values until the plot is visible.
A researcher want to interview two people who use busses.
The research gets on two different busses and selects people at random.
The probability that a person is male on the 1st bus is 9/15
The probability that a person is male on the 2nd bus is 7/15
Find the probability that both people picked are female.
Divide the polynomials
Answer:
[tex]\frac{2x^{4} - 5x^{2} + x + 6 }{x}[/tex]
Step-by-step explanation:
[tex]\frac{2x^{3} - 5x + \frac{6}{x} + 1 }{x}[/tex]
[tex]\frac{2x^{4} - 5x^{2} + x + 6 }{x}[/tex]
[tex]2 {x}^{2} - 2x - 3[/tex]
step by step explanations
Please help me!!!!!!!
Answer:
Below
Step-by-step explanation:
The ENTIRE CIRCLE arc length (360° circumference ) is given by pi * 2 r
= pi * 2 * 10 = 20 pi cm
We want to find 299 out of 360ths of this
299/360 * 20 pi = ~ 52.2cm
A researcher is evaluating the effectiveness of a new physical education program for elementary school children. The program is designed to reduce competition and increase individual self-esteem. A sample of n=36 children is selected and the children are placed in the new program. After 3 months, each child is given a standardized self-esteem test. The mean is M=43. For the general population of elementary school children, the scores on the self-esteem test are normally distributed with μ = 40 and σ = 8 . Conduct a two-tailed one-sample z-test at the α = .05 level.
a, State the null and alternative hypotheses in words and symbols.
b. Conduct the hypothesis test (use both the critical value and p-value approach). Show steps 3 and 4 of hypothesis testing.
If appropriate, compute and interpret Cohen’s d.
State the conclusion of your hypothesis test.
The mean self-esteem score after the program (M = 43) is not significantly different from the population mean self-esteem score (μ0 = 40) at the α = 0.05 level.
what is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain.
a. The null hypothesis (H0) is that the new physical education program has no effect on the self-esteem scores of elementary school children, or in other words, the mean self-esteem score after the program (μ) is equal to the population mean self-esteem score (μ0): H0: μ = μ0 = 40.
The alternative hypothesis (Ha) is that the new program has an effect on the self-esteem scores, either positive or negative, or in other words, the mean self-esteem score after the program (μ) is not equal to the population mean self-esteem score (μ0): Ha: μ ≠ μ0.
b.
Step 1: Set up the hypothesis:
H0: μ = μ0 = 40
Ha: μ ≠ μ0
Step 2: Determine the significance level: α = 0.05
Step 3: Calculate the test statistic:
z = (M - μ0) / (σ / sqrt(n))
z = (43 - 40) / (8 / sqrt(36))
z = 1.5
Step 4: Determine the critical value or p-value:
For a two-tailed test with α = 0.05, the critical values are -1.96 and 1.96.
Since the calculated test statistic (z = 1.5) is not in the rejection region (it falls between -1.96 and 1.96), we fail to reject the null hypothesis.
Alternatively, we can calculate the p-value using a standard normal distribution table or a calculator. The p-value for a two-tailed test with z = 1.5 is 0.134. Since the p-value is greater than the significance level (p > α), we fail to reject the null hypothesis.
Cohen's d can be calculated as d = (M - μ0) / s, where s is the standard deviation of the population.
d = (43 - 40) / 8 = 0.375
This means that the mean self-esteem score of the sample is 0.375 standard deviations higher than the population mean self-esteem score.
Therefore, The mean self-esteem score after the program (M = 43) is not significantly different from the population mean self-esteem score (μ0 = 40) at the α = 0.05 level.
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A standard number cube is rolled 150 times. Predict how many times it will roll a 1 or a 6.
Answer:
100 times
Step-by-step explanation:
It is predicted that a 1 or a 6 will be rolled 50 times in 150 rolls of a standard number cube.
A standard number cube has six faces, each numbered from 1 to 6.
The probability of rolling a 1 or a 6 on any given roll is,
P = 2/6
P = 1/3
Since, there are two favorable outcomes out of six possible outcomes.
Hence, To predict how many times a 1 or a 6 will be rolled in 150 rolls, we can use the formula:
Number of times = Probability x Total number of rolls
So, the number of times a 1 or a 6 is expected to be rolled in 150 rolls is:
Number of times = (1/3) x 150 = 50
Therefore, it is predicted that a 1 or a 6 will be rolled approximately 50 times in 150 rolls of a standard number cube.
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a footrace takes place among four runners. if ties are allowed (even all four runners finishing at the same time), how many ways are there for the race to finish?
The race can finish in 256 possible ways, accounting for the possibility of ties among the four runners.
There are 4 runners in the race and any of them can finish first, so there are 4 ways to choose the winner. Once the winner is chosen, there are 4 remaining runners who can finish in second place.
Therefore, there are 4 × 4 = 16 ways for the first two places to be filled.
Once the first two places are filled, there are 4 remaining runners who can finish in third place.
Therefore, there are 4 × 16 = 64 ways for the first three places to be filled.
Finally, once the first three places are filled, there are 4 remaining runners who can finish in fourth place.
Therefore, there are 4 × 64 = 256 ways for all four runners to finish the race.
Therefore, there are 256 ways for the race to finish, including ties.
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A trapezoid has a base of 5 millimeters,
another base of 7 millimeters, and a height
of 6 millimeters. Explain how the area of the
trapezoid will change if the height and both
bases are doubled.
The area of the trapezoid is multiplied by a factor of 4 when both bases and the height are doubled.
What is trapezoid ?Trapezoids can be defined as quadrilaterals that have two parallel sides and two non-parallel sides.
The area of a trapezoid is given by the formula:
A = (b1 + b2) * h / 2
Where
b1 and b2 are the lengths of the two basesh is the heightIf we double both bases and the height, we get:
b1' = 2 * b1 = 2 * 5 mm = 10 mm
b2' = 2 * b2 = 2 * 7 mm = 14 mm
h' = 2 * h = 2 * 6 mm = 12 mm
Now we can calculate the area of the new trapezoid:
A' = (b1' + b2') * h' / 2
A' = (10 mm + 14 mm) * 12 mm / 2
A' = 12 * 12 mm^2
A' = 144 mm^2
Therefore, the area of the trapezoid is multiplied by a factor of 4 when both bases and the height are doubled.
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Two angles of a quadrilateral measure 140° and 60°. The other two angles are in a ratio of 7:9. What are the measures of those two angles?
In the quadrilateral the measure of angles in ratio 7 : 9 is 70° and 90°. respectively.
What is an angle?
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
The sum of the angles of a quadrilateral is always 360 degrees.
So, we can start by finding the measure of the two unknown angles using the information that we have -
Let x be the measure of the smaller of the two unknown angles, then the measure of the larger angle is 9x and smaller angle is 7x (since the two angles are in a ratio of 7:9).
The sum of all four angles is 140° + 60° + 7x + 9x = 360°.
Simplifying this equation, we get -
140° + 60° + 16x = 360°
200° + 16x = 360°
16x = 160°
Dividing both sides by 16, we get -
x = 10°
So, the smaller of the two unknown angles is -
7x = 7 × 10° = 70°
The larger angle is -
9x = 9 × 10° = 90°
Therefore, the measures of the two unknown angles are 70° and 90°.
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many people use scanners to read documents and store them into pdf file. to help determine which brand of scanner to buy, a student conducts an experiment in which 8 different documents were scanned by each of the two scanners that he is interested in. he records the number of errors made by each. can he infer that brand a (the more expensive scanner) is better than brand b? that is, is the mean number of errors for brand a less than brand b? use brand a as population 1 and brand b as population 2. assume a 5% level of significance. dat
The student can use a two-sample t-test to determine if there is a significant difference between the mean number of errors made by brand A and brand B. The two-sample t-test compares the means of two populations to determine if they are significantly different from each other.
The null hypothesis for this test is that the mean number of errors for brand A is equal to the mean number of errors for brand B. The alternative hypothesis is that the mean number of errors for brand A is less than the mean number of errors for brand B.
To conduct the two-sample t-test, the student will need to calculate the mean and standard deviation of the number of errors for each brand. Then, he will use the t-test formula to calculate the t-value and compare it to the critical value for a 5% level of significance.
If the t-value is less than the critical value, the student can reject the null hypothesis and conclude that the mean number of errors for brand A is significantly less than the mean number of errors for brand B. This would suggest that brand A is better than brand B.
However, if the t-value is greater than the critical value, the student cannot reject the null hypothesis and cannot conclude that there is a significant difference between the two brands.
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In the data set below, what is the interquartile range?
34 60 65 70 72
Answer:
The Interquartile Range or (IQR) is 24
Step-by-step explanation:
Since the data set is ordered, we don't need to order it.
Now, to find the interquartile range:
First, find median which is 65 since it is in the middle
Next, we find the median in Quartile 1 and Quartile 3 (Quartile 2 is median)
So in Quartile 1, median is 47
Quartile 2, median is 71
Now find the range of those two:
71 - 47 = 24
Hope this helps!!
What is the median below?
Answer:2.6
Step-by-step explanation:
in order to find median you should sort your numbers first.
so our sorted numbers would be,
0.4 0.9 1.1 1.1 2.6 2.7 3.5 5.7 9.8
find middle element,
0.4 0.9 1.1 1.1 2.6 2.7 3.5 5.7 9.8
2.6 is median
In 8 years Harry and Sally would like to have $12000 for a down payment on a house. How much should they deposit each month
into an account paying an annual interest rate of 11% compounded monthly?
Answer =
Answer: 5 percent
Step-by-step explanation:
Step-by-step explanation:
1year=12month
8years =12×8=86month
11/100×12000=1320
12000-1320=10680
10680/86
they will deposit 124
Paisley needs to order some new supplies for the restaurant where she works. The restaurant needs at least 521 spoons. There are currently 225 spoons. If each set on sale contains 15 spoons, which inequality can be used to determine s, the minimum number of sets of spoons Paisley should buy? ○ 15s +225 521 15 +225s 2521 O 158 +225 2 521 O 15 +2258 ≤ 521
Answer:
15s + 225 is less than or equal to 521
Step-by-step explanation:
The restaurant needs 521 spoons and it only has 225.
There is a very simple answer for this.
If each set on sale contains 15 spoons (algorithm rule)
So determine s (15 x s) = 15s (calculation principle)
then 15s + 225 is less than or equal to 521
therefore the result is 15s + 225 is less than or equal to 521 spoons
What is the difference?complete the stament -2-8=
Answer: -10
Step-by-step explanation: You're welcome <3