The ratio of girls to boys at a party is 5:4. if there are 20 girls in the class, how many boys are there.

The surface area of the prism is 544 mm²

The formula is given thus;

SA=2B+ph

Where

B = area of the base

p = perimeter of the base

h = height

B = 1/2 h(b1+b2)

B = [tex]\frac{1}{2} * 8 * (17 + 9)[/tex]

B = 108 mm²

Perimeter = sum of length of sides

Perimeter = 17 + 9 + 15

Perimeter = 41 mm

Surface area = 2 ( 108 ) + 41 ( 8)

Surface area = 216 + 328

Surface area = 544 mm²

Thus, the surface area of the prism is 544 mm²

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Answer:

Option c is the correct answer

Step-by-step explanation:

distance of satrun - distance of jupiter

Answer:

Step-by-step explanation:

    p=-12x^2 + 168 - 510        

   isolate the varible by diveding each side by factors that dont conatin the varible

x= square root of -p+342/3/2

x= - square root of  -p+ 342/3/2

I hope this has helped if you need any clarfcation just ask

The data is significant at a significance level of 0.01 indicating that the average mass of apples in a farmer's orchard differs from 100g to a level of 0.01. Option C is correct.

Given as the farmer states that the average mass of an apple grown in his orchard is 100g, he measures the mass of 150 apples grown in his orchard and finds that the average mass per apple is 98g and the results are calculated as statistically significant at the 0.01 level.

The null hypothesis is:

H₀ = 100

Because of the farmer's claim.

The alternative hypothesis is:

H₁ ≠ 100

The alternative hypothesis tests the farmer's claim at a level of significance. Results are calculated as statistically significant at the 0.01 level.

This means that at the 0.01 level, the null hypothesis is rejected, i.e. H the average mass of the farmer's orchard differs from 100. Since it is significant at the 0.01 level, it will be significant at the 0.05, 0.1 and increasing levels.

Thus, at the significance level of 0.01, the average mass of apples grown in the farmer's orchard differs by 100 g. The correct answer is therefore given by option C.

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Answer:

12 / (2+1) + 6 * 2 = 16 (The answer is 16)

Step-by-step explanation:

Step 1: Calculate within parentheses ( 2 + 1 ) : 3

= 12/3 + 6 * 2

Step 2: Multiply and divide (left to right) 12/3 : 4

= 4 + 6 * 2

Step 3: Multiply and divide (left to right) 6 * 2 : 12

= 4 + 12

Step 4: Add and subtract (left to right) 4 + 12 : 16

= 16

Hope this helps out!

The graph represents the type of power function of the form y = kx in the form of D. Inverse Variation with an even r-value & a positive k-value.

It should be noted that a graph simply means a diagrammatic representation of a particular thing.

Here, the function of the for y = kx is illustrated in the graph.

This is an inverse variation with an even r-value and a positive k-value.

In conclusion, the correct option is D.

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The probability that the call center will get fewer calls than 440 is 0.26115.

Given mean of 4900 and standard deviation of 700.

We have to calculate the probability that the call center will get fewer than 4400 calls.

Probability lies between 0 and 1.

μ=4900

σ=700

We can  apply z as well as t statistics because the sample size is not given.

We are applying z statistics.

P(X<4400)=0.5-P(4400<X<4900)

z=X-μ/σ

where μ= mean

σ=standard deviation

z=4400-4900/700

=-500/700

=-0.71

p value of -0.71 is 0.23885.

So the p value of calls less than 4400 is 0.5-0.23885=0.26115.

Hence the probability that the call center will get calls less than 440 is 0.26115.

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Answer:

Θ ≈ 58°

Step-by-step explanation:

using the Cosine Rule in the triangle

cosΘ = [tex]\frac{80^2+60^2-70^2}{2(80)(60)}[/tex] = [tex]\frac{64000+3600-4900}{9600}[/tex] = [tex]\frac{5100}{9600}[/tex] = [tex]\frac{51}{96}[/tex] , then

Θ = [tex]cos^{-1}[/tex] ( [tex]\frac{51}{96}[/tex] ) ≈ 58° ( to the nearest degree )

Answer:

False

Step-by-step explanation:

[If two lines are perpendicular, then the lines intersect to form four right angles] It's true up till here, but a right angle is 90 degrees, not 180 degrees

The measure for the unknown angle is 65 degrees.

The two perpendicular lines form a right angle. A right angle would always have a value of 90 degrees.

In order to determine the unknown angle, subtract 25 degrees from 90 degrees.

90 - 25 = 65 degrees

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New mean is 2.53% larger than the original mean.

What is mean?

Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set.

We can find the percentage larger is the mean of the new list in comparison with the original as shown below:

Given, set of number 55, 70, 81, 83, 88, 91

Median= (81+83)/2

= 164/2

= 82

Mean = (55+70+81+83+88+91)/6

= 468/6

= 78

New value which is added = 82*1.12

= 91.84

New Mean = (55+70+81+83+88+91+91.84)/7

= 559.84/7

= 79.97

Increase in mean = 79.97-78

=1.97

increase percentage (1.97/78) *100

= 2.53%

Hence, new mean is 2.53% larger than the original mean.

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TRUE

The fatal accident rate for young drivers aged 16 to 19 is about four times higher than at night. Two or more passengers of the same age triple the risk of a fatal accident driving a teenager.

An accident in which someone dies. Synonyms: Accident. Type: Collateral damage.

Of the collisions between cars, angled collisions are the most deadly (about 8,000 in 2020). The interactive chart also shows the estimated number of fatalities, injuries, casualties, and all accidents in different types of car accidents.

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A journalist's statement about this piece of information after analyzing the data could be (a) the owner made a mistake because the rate is constant

From the question, we have the following highlights:

From the graph attached to the question, we can see that the graph that shows the tons of sugar Bel sugar mill fabricated from its opening day in 2008 to 2013 is a linear graph

This is so because the points on the graph are connected by a straight line.

Linear graphs have constant rate

Hence, a journalist's statement about this piece of information after analyzing the data could be (a) the owner made a mistake because the rate is constant

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Complete question

The following graph shows the tons of sugar Bel sugar mill fabricated from its opening day in 2008 to 2013. The owner of the sugar mill said in an interview that the production increased at an exponential rate since the inauguration. What would a journalist say about this piece of information after analyzing the data?

Answer:

a = -1

Step-by-step explanation:

1. Subtract [tex]\frac{2}{3}[/tex] from both sides.

[tex]6a=-\frac{16}{3} - \frac{2}{3}[/tex]

2. Solve the side after the equal sign.

[tex]6a=-6[/tex]

3. Divide 6 from both sides.

[tex]a=-1[/tex]

4. Hope this helped!

[tex]:)[/tex]

The law of sines cannot be used to calculate the side c.

The given parameters are:

A = 27.5°, a = 15.0 cm, b = 36.4 cm

Based on the above values,

The law of sines cannot be used to calculate the side c.

This is so because the angle C is not given

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Answer:

Step-by-step explanation:

5x = 140

= x = 140/5

= x = 28

Answer:

five number summary is a specially useful in the scriptive analysing what during the premier league investigation of a large data set a summary consists of 5 values of the most extreme values in data set the maximum and minimum values of the lower and upper quality and the meridian

The display that would best show the measures of variation of the given prices is; B: Box and Whisker Plot

We are given the prices of Phone chargers in a store as;

$19, $18, $15, $17, $19, $12, $19, and $15.

Now, since we want to determine the display that would best show the measures of variation, the best display would be a box and whisker plot. This is because Box and Whisker plots are a great chart to use when showing the distribution of data points across a selected measure. These  box and whisker plots display ranges within variables measured.

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Answer:

20%

Step-by-step explanation:

To find the percentage of change find the difference between the two numbers, divide by the original number, then multiply by 100.

Find difference

90-72=18

Divide difference by original

18/90=0.2

Multiply by 100

0.2*100=20

The measure of angle C is obtained as 35 degrees

Give that;

b^2 = a^2 + c^2 - 2ac Cos B

a = 29

c = 24

B = 101 degrees

b^2 = (29)^2 + (24)^2 - [2 * 29 * 24 cos 101]

b^2 = 841 + 576 + 266

b = 41 cm

Now;

b/sinB = c/sinC

bsinC = csinB

sinC = csinB/b

sinC =  24 * sin 101/41

C = sin-1(24 * sin 101/41)

C = 35 degrees

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Answer: [tex]y=-2x+6[/tex]

Step-by-step explanation:

The slope of line l is

[tex]\frac{5-1}{0-2}=-2[/tex]

Since parallel lines have the same slope, the slope of the line we need to find is -2.

Substituting into point-slope form,

[tex]y=-2(x-3)\\\\y=-2x+6[/tex]

Hello,

[tex] \frac{5}{4 - m} = \frac{ - 3}{2 + m} [/tex]

[tex]5(2 + m) = - 3(4 - m)[/tex]

[tex]10 + 5m = - 12 + 3m[/tex]

[tex]5m - 3m = - 12 - 10[/tex]

[tex]2m = - 22[/tex]

[tex]m = \frac{ - 22}{2} [/tex]

[tex]m = - 11[/tex]

→ Answer B

Variable m cannot be equal to any of the values −2,4 as division by zero is undefined. Multiply both sides of the equation by (m − 4)(m + 2), the lowest common denominator of 4−m,m + 2.

To find the opposite of 2+m, find the opposite of each term.

Use the distributive property to multiply −2−m by 5.

Use the distributive property to multiply m−4 by −3.

Add 3m to both sides.

Combine −5m and 3m to get −2m.

Add 10 to both sides.

Add 12 and 10 to get 2.

Divide both sides by −2.

Divide 22 by −2 to get −11.

Therefore, the correct option is "B".

The value of a + b + c based on the product formula is 8.

From the information given, the product of the proper divisor is illustrated.

Based on the information, the addition of the symbols will be:

= a + b + c

= 3 + 3 + 2

= 8

In conclusion, the correct option is 8.

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We cannot reject the null hypothesis as the p value is less than 0.01.

From the information given, Luiza wants to go on a popular talent TV show and in order to be accepted, her audition must get at least 60% positive votes from the people in the crowd.

The observed outcome also has a probability less than 1% under the tested hypothesis. Based on the information, the test statistic will be - 1.58.

After this, this will be checked under the standard normal distribution table where the p value will be 0.0571.

Based on this information, we cannot reject the null hypothesis as the p value is less than 0.01.

In conclusion, the correct option is that we cannot reject the hypothesis.

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If JJ decided to leave a tip that is 15% of the original price for his meal, he should leave $1.2 as tip for the $5.50 cheeseburger and $2.50 milkshake.

According to this question, JJ bought a $5.50 cheeseburger and a $2.50 milkshake.

This means that in total, JJ purchased $5.50 + $2.50 = $8 worth of meal.

If he decided to leave a tip that is 15% of the original price of his meal, hence,

15/100 × $8 = $1.2

Therefore, if JJ decided to leave a tip that is 15% of the original price for his meal, he should leave $1.2 as tip for the $5.50 cheeseburger and $2.50 milkshake.

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The measure of the largest side of an isosceles acute triangle with one side of 36 degrees is 72 degrees.

A triangle with two sides and angles of equal length and degrees is an isosceles triangle.

Acute Triangle:-

A triangle whose all angels are greater than and less than 90° i.e., all angels are acute is called an acute triangle.

Therefore, all the three angles are less than 90 degrees and two angles are equal.

If one angle is 36 degrees, the other two angles will be 72 degrees each.

If the two angles are 36 degrees each, the last angle will be 108 degrees. 108 degrees is greater than 90 degrees..

Therefore, the angles will be 36°, 36° and 72°.

Hence, the measure of the largest side of an isosceles acute triangle with one side of 36 degrees is 72 degrees.

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The arrangement of the numbers in descending order (largest to smallest) are as follows;

It follows from convention that the positive numbers are larger than negative numbers and hence, should appear before negative numbers when the arrangement is in descending order.

Consequently, the numbers can be evaluated and arranged as in the answer above with positive numbers increasing rightwards and negative numbers decreasing leftward of 0 on the number line.

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Answer:

Letters A, M, and T

Step-by-step explanation:

All of these letters have a point of symmetry.

Answer: m

Step-by-step explanation:

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{-8 < 3x+1 < 13 }} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{-8+-1 < 3x+1+-1 < 13+-1 \ (Add \ -1 \ to \ all \ parts) }} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{-9}{3} < \frac{3x}{3} < \frac{12}{3} \ (Divide \ all \ parts \ by \ 3) }} \end{gathered}$}[/tex]

[tex]\red{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{-3 < x < 4 }} \end{gathered}$} }}[/tex]