what expression is equal to -4x²-36?

Answer:

Exterior and interior angles are supplementary, meaning they sum to 180 degrees. If the exterior and interior angles are x and 5x respectively, we can write x + 5x = 180, and solving for x we get x = 30°. This means that the answer to a) is 30° and the answer to b) is 30 * 5 = 150°.

For c), to find the number of sides we can do:

180 - 150 = 30

180 / 30 = 6 so the answer to c) is 6.

Answer:

13 goats and 23 cows

Step-by-step explanation:

Use x to solve :) it's a hint

Answer:

g=goats

c=cows

a=cars

g + c = 36

10 + g = a

Step-by-step explanation:

the number of cows and goats together are equal to 36, so for the first equation you can write g + c = 36.

For the second equation, the number of cars he has is equal to the number of goats he has plus 10, so you can express that as 10 + g = a. (I used a since I already used c for the cows)

I think this is what you need if you need 2 equations to represent how many cars he has.

I'm not entirely sure what its asking you can comment if you need more or something else.

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A tangent to a circle forms a right angle with the radius

As it is a right angled triangle, we can use Pythagoras' theorem

a^2 + b^2 = c^2

Rearrange this for a side length:

a^2 = c^2 - b^2

Sub the values in:

a^2 = 6.5^2 - 6^2

a^2 = 6.25

Square root this for the answer

a = 2.5

Thus, your answer is option D

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Answer:

2.5 ft

Step-by-step explanation:

As radius is perpendicular to tangent ,

LT [tex]\perp[/tex]KT

By pythagoras theorem:

LT² = LK² - KT²

LT² = (6.5)² - 6²

LT² = 42.25 - 36

LT² = 6.25

LT = 2.5 ft

LT = radius = 2.5 ft

Answer:

0

Step-by-step explanation:

The 0, or the last digit is the insignificant digit because it serves no purpose.

Answer:

The last zero in the number is insignificant.

Step-by-step explanation:

The 0 at the extreme right indicates that the number is accurate to the fifth decimal place, that is, one in ten thousandths.

[tex](x1,y1)= (- \frac{\sqrt{15} }{2} , \frac{5}{4} )\\(x2,y2)= (\frac{\sqrt{15} }{2} ,\frac{5}{4} )[/tex]

Answer:

Answer C.

Step-by-step explanation:

hope this helps <3

Answer:

Loading/unloading hourly rate: $70

Packing/unpacking hourly rate: $55

Step-by-step explanation:

We can write this as a system of linear equations.

We define L as the loading/unloading hourly rate, and P as the packing/unpacking hourly rate.

"One quote was for a weekday move which is  for 8 hours of loading/unloading and 6 hours of packing/unpacking for $890":

[tex]8L+6P=890[/tex]

"The other quote was for a  weekend move which is for 5 hours of loading/unloading and 3 hours of packing/unpacking for $515":

[tex]5L+3P=515[/tex]

If we express L in function of P in the first equation, and then replace this value in the second equation, we have:

[tex]8L+6P=890\\\\8L=890-6P\\\\L=\dfrac{890-6P}{8}[/tex]

[tex]5L+3P=515\\\\5\cdot \dfrac{890-6P}{8}+3P=515\\\\556.25-3.75P+3P=515\\\\-0.75P=515-556.25=-41.25\\\\P=41.25/0.75=55[/tex]

Then, L is:

[tex]L=\dfrac{890-6P}{8}=\dfrac{890-6(55)}{8}=\dfrac{890-330}{8}=\dfrac{560}{8}=70[/tex]

ABC and DEC are similar, since the line segments AB and DE are parallel.

This means corresponding sides of these triangles occur in a fixed ratio with one another.

In particular, this tells us

DE/AB = DC/AC

or

7/11 = 15/(15 + x)

Solve for x:

11/7 = (15 + x)/15

11/7 = 1 + x/15

4/7 = x/15

x = 60/7

Answer:

Step-by-step explanation:

A quart is 1/4 gallon, so the total of liquid ingredients for the punch is ...

  (1 2/4 gal) +(3/4 gal) +(1 3/4 gal) = 2 8/4 gal = 4 gal

Samantha made 4 gallons of punch.

__

1 cup is 1/16 gallon, so 2 cups each for 25 students requires ...

  (1/16 gal)(2)(25) = 50/16 gal = 3 1/8 gal

Samantha made more punch than that, so there will be enough for 2 1-cup servings for each student.

Answer:

10 units

Explanation:

Create a right triangle, determine the a and b side lengths of the triangle by looking at the graph. (See image)

Then use the Pythagorean theorem to find c.

a² + b² = c²

(8)² + (6)² = c²

64 + 36 = c²

100 = c²

Square root both sides to get c.

[tex]\sqrt{100}[/tex] = c

10 = c

Solution:

12.5 < x < 18.9

Reason:

To solve this problem, we can apply Pythagorean's theorem.

To find the upper bound:

We can set the two given legs as the 2 legs of a right triangle. This allows us to keep the angle under 90 degrees. So if we set the legs to be 10 and 16, then the third side must be:

10^2 + 16^2 = x^2

x^2 = 356

x is roughly equal to 18.9

For the lower bound, this time, we set x as one of the legs, and 10 as the other let. Since we know that the longest side is 16, we can set up an equation again:

x^2 + 10^2 = 16^2

x^2 = 16^2 - 10^2

x^2 = 156

x is roughly equal to 12.5

So we have found the bounds to be 12.5 < x < 18.9

Answer:

its B

Step-by-step explanation:

Answer:

a) We are told smaller scores indicate a more feminine scent and larger scores a more masculine scent, also a score of 12 represents a gender-neutral scent.

Here the average from the sample for lavender is 10.28

To test for the evidence that lavender is not gender neutral on average, the null hypothesis H0 would take that lavender is gender-neutral, while the alternative hypothesis would take that the score of lavender is not gender neutral. We now have the null and alternative hypotheses as:

H0 : u = 12

H1 : u ≠ 12

Here, u represents the mean gender-orientation score for lavender. The alternative is two sided because we want to test if lavender is not gender neutral. Which means lavender might be more masculine of more feminine.

b) Given: p < 0.01 (2 tailed)

This means the p-value is less than level of significance 0.01.

Since the pvalue is less than the level of significance, we reject null hypothesis H0. This means there is sufficient evidence to conclude that the smell is not gender-neutral.

There is no reason to prefer a particular gender, that's why this is a two tailed hypothesis.

c) c.Assuming that the conditions for inference were met, which means the p-value is less than 0.01 so the null hypothesis H0 is rejected.

The conlusion would be that there is enough evidence to conclude that lavender is not gender-neutral

Answer:

11*20!

Step-by-step explanation:

(20!+21!+22!)/44=

20!(1+21+21*22)/44=

20!(22+22*21)/44=

20!*22*22/44= 11*20!

The simplified expression of (20!+21!+22!)/44 is 20! * 11

The expression is given as:

(20!+21!+22!)/44

The factorial of a number n is:

n! = n * (n - 1)!

So, we start by expanding 22!

(20!+21!+22!)/44 = (20!+21!+22 * 21 * 20!)/44

Next, we expand 21!

(20!+21!+22!)/44 = (20!+21 * 20!+22 * 21 * 20!)/44

Factor out 20!

(20!+21!+22!)/44 = 20! * (1 + 21 + 22 * 21)/44

Evaluate the expression in the bracket

(20!+21!+22!)/44 = 20! * 484/44

Divide

(20!+21!+22!)/44 = 20! * 11

Hence, the simplified expression of (20!+21!+22!)/44 is 20! * 11

Read more about simplified expression at:

https://brainly.com/question/723406

#SPJ6

Answer:

[tex] \sqrt{55}[/tex]

Step-by-step explanation:

Given is a right angled triangle.

Therefore, by Pythagoras theorem:

[tex] {x}^{2} = {8}^{2} - {3}^{2} \\ = 64 - 9 \\ = 55 \\ x = \sqrt{55} [/tex]

Answer:

Step-by-step explanation:

there is a pressure difference between inside and outside the container and if the — bag, bottle, whatever — is flexible enough it will either expand as the ambient air pressure decreases when climbing or collapse when the aircraft is descending and the pressure is increasing.......

this is ur answer ....

Answer:

20

Step-by-step explanation:

x is the radius of the circle.  The tangent line is perpendicular to the radius line at that point.  Using Pythagorean theorem:

x² + 15² = (x + 5)²

x² + 225 = x² + 10x + 25

225 = 10x + 25

200 = 10x

x = 20

Answer is:

x = 20. hope this helps

Here is  the correct computation of the question given.

Find the coefficient of variation for each of the two sets of data, then compare the variation. Round results to one decimal place. Listed below are the systolic blood pressures (in mm Hg) for a sample of men aged 20-29 and for a sample of men aged 60-69.

Men aged 20-29:      117      122     129      118     131      123

Men aged 60-69:      130     153      141      125    164     139

Group of answer choices

a)

Men aged 20-29: 4.8%

Men aged 60-69: 10.6%

There is substantially more variation in blood pressures of the men aged 60-69.

b)

Men aged 20-29: 4.4%

Men aged 60-69: 8.3%

There is substantially more variation in blood pressures of the men aged 60-69.

c)

Men aged 20-29: 4.6%

Men aged 60-69: 10.2 %

There is substantially more variation in blood pressures of the men aged 60-69.

d)

Men aged 20-29: 7.6%

Men aged 60-69: 4.7%

There is more variation in blood pressures of the men aged 20-29.

Answer:

(c)

Men aged 20-29: 4.6%

Men aged 60-69: 10.2 %

There is substantially more variation in blood pressures of the men aged 60-69.

Step-by-step explanation:

From the given question:

The coefficient of variation can be determined by the relation:

[tex]coefficient \ of \ variation = \dfrac{standard \ deviation}{mean}*100[/tex]

We will need to determine the coefficient of variation both men age 20 - 29 and men age 60 -69

To start with;

The coefficient of men age 20 -29

Let's first find the mean and standard deviation before we can do that ;

SO .

Mean = [tex]\dfrac{\sum \limits^{n}_{i-1}x_i}{n}[/tex]

Mean = [tex]\frac{117+122+129+118+131+123}{6}[/tex]

Mean = [tex]\dfrac{740}{6}[/tex]

Mean = 123.33

Standard deviation  [tex]= \sqrt{\dfrac{\sum (x_i- \bar x)^2}{(n-1)} }[/tex]

Standard deviation =[tex]\sqrt{\dfrac{(117-123.33)^2+(122-123.33)^2+...+(123-123.33)^2}{(6-1)} }[/tex]

Standard deviation  = [tex]\sqrt{\dfrac{161.3334}{5}}[/tex]

Standard deviation = [tex]\sqrt{32.2667}[/tex]

Standard deviation = 5.68

The [tex]coefficient \ of \ variation = \dfrac{standard \ deviation}{mean}*100[/tex]

[tex]coefficient \ of \ variation = \dfrac{5.68}{123.33}*100[/tex]

Coefficient of variation = 4.6% for men age 20 -29

For men age 60-69 now;

Mean = [tex]\dfrac{\sum \limits^{n}_{i-1}x_i}{n}[/tex]

Mean = [tex]\frac{ 130 + 153 + 141 + 125 + 164 + 139}{6}[/tex]

Mean = [tex]\dfrac{852}{6}[/tex]

Mean = 142

Standard deviation  [tex]= \sqrt{\dfrac{\sum (x_i- \bar x)^2}{(n-1)} }[/tex]

Standard deviation =[tex]\sqrt{\dfrac{(130-142)^2+(153-142)^2+...+(139-142)^2}{(6-1)} }[/tex]

Standard deviation  = [tex]\sqrt{\dfrac{1048}{5}}[/tex]

Standard deviation = [tex]\sqrt{209.6}[/tex]

Standard deviation = 14.48

The [tex]coefficient \ of \ variation = \dfrac{standard \ deviation}{mean}*100[/tex]

[tex]coefficient \ of \ variation = \dfrac{14.48}{142}*100[/tex]

Coefficient of variation = 10.2% for men age 60 - 69

Thus; Option C is correct.

Men aged 20-29: 4.6%

Men aged 60-69: 10.2 %

There is substantially more variation in blood pressures of the men aged 60-69.

Given that we have 47 kids and each kid needs 10 marbles, find out how many bags of 24 marbles will we need.

First, we will multiply 47 by 10 to get the amount of marbles needed.

47 x 10 = 470

So, that means we need 470 marbles in total.

Then, we divide 470 by 24 to see how many bags of 24 marbles 470 marbles is.

470 / 24 = 19.5833

Since, we can't have 19.5833 bags, we have to check what it would be if we only used 19.

19 x 24 = 456

470 - 456 = 14

Since, 18 is the closest number of bags but it has less than 470 it would not be correct.

Therefore, the best answer would be B. 25 since it is better to have extra marbles but not a very wide margin.

Answer:

$1946

Step-by-step explanation:

Eric’s average income for the first 4 months of the year is $1,450.25

Therefore, his total earning in the first four months

= 4 X $1,450.25

=$5,801

Let the average income for the remaining 8 months= x

Then:

[tex]\text{Eric's Yearly Average Income}=\dfrac{5801+8x}{12} \\1,780.75=\dfrac{5801+8x}{12} \\$Cross multiply\\12*1,780.75=5801+8x\\21369=5801+8x\\8x=21369-5801\\8x=15568\\Divide both sides by 8\\x=\$1946[/tex]

Therefore, to get an average income for the year of $1,780.75, Eric must earn an average income of $1946 for the remaining 8 months.

Answer:

12h < 60

Step-by-step explanation:

A rectangle, with height h and base length l, has the following area.

[tex]A = l*h[/tex]

In this question:

[tex]l = 12, A < 60[/tex]

So

[tex]A < 60[/tex]

[tex]l*h < 60[/tex]

[tex]12h < 60[/tex]

So the correct answer is:

12h < 60

Answer:

12h < 60

hope this helps, its right because i took the test and it shows

Answer:

£77.6 per day

Step-by-step explanation:

388/5 = 77.6

Answer:

£77.60

Step-by-step explanation:

388/5=77.6

but remember that this is money so add the 0.

Answer:

The solutions for the equations are x = 0.1644 and x = -12.1644

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

In this question:

[tex]x^{2} + 12x - 2 = 0[/tex]

So

[tex]a = 1, b = 12, c = -2[/tex]

[tex]\bigtriangleup = 12^{2} - 4*1*(-2) = 152[/tex]

[tex]x_{1} = \frac{-12 + \sqrt{152}}{2} = 0.1644[/tex]

[tex]x_{2} = \frac{-12 - \sqrt{152}}{2} = -12.1644[/tex]

The solutions for the equations are x = 0.1644 and x = -12.1644

Answer:

Step-by-step explanation:

Twenty-five percent of thirty dollars is $7.50

(30 x 25)/100 = $7.50

Thirty percent of twenty-five dollars is $7.50

(25 x 30)/100 = $7.50

Therefore he is right

I hope this helps

Answer:

A. T > 2.539

Step-by-step explanation:

We have a hypothesis test of the mean, with unknown population standard deviation.

The hypothesis are:

[tex]H_0: \mu = 2.1 \\\\H_a: \mu > 2.1[/tex]

From the hypothesis we can see that the test is right-tailed, so the critical value of t should be a positive value.

The degrees of freedom can be calculated as:

[tex]df=n-1=20-1=19[/tex]

The significance level is 0.01, so the critical value tc should be the one that satisfies:

[tex]P(t>t_c)=0.01[/tex]

Looking up in a t-table, for 19 degrees of freedom, this critical value is tc=2.539.

Answer:

There is sufficient statistical evidence to prove that the standard deviation of the technology-related workers and the standard deviation of the non-technology workers are equal.

Step-by-step explanation:

Here we have our null hypothesis as H₀: σ² = s²

Our alternative hypothesis is then Hₐ: σ² ≠ s²

We therefore have a two tailed test

To test the hypothesis of difference in standard deviation which is the Chi squared test given as follows

[tex]\chi ^{2} = \dfrac{\left (n-1 \right )s^{2}}{\sigma ^{2}}[/tex]

Where:

n = Size of sample

s² = Variance of sample = 950²

σ² = Variance of population = 650²

Degrees of freedom = n - 1 = 71 - 1 = 70

α = Significance level = 0.1

Therefore, we use 1 - 0.1 = 0.9

From the Chi-square table, we have the critical value as

1 - α/2 = 51.739,  

α/2 = 90.531

Plugging the values in the above Chi squared test equation, we have;

[tex]\chi ^{2} = \dfrac{\left (23-1 \right )950^{2}}{650 ^{2}} = 49.994[/tex]

Therefore, since the test value within the critical region, we do not reject the null hypothesis, hence there is sufficient statistical evidence to prove that the standard deviation of the technology-related workers and the standard deviation of the non-technology workers are equal.

Answer:

[tex]M(t) = 175(0.9943)^{t}[/tex]

Step-by-step explanation:

The amount of kryptonite-344 after t days is given by the following equation:

[tex]M(t) = ab^{t}[/tex]

In which a is the initial amount.

175g sample:

This means that [tex]a = 175[/tex]

So

[tex]M(t) = 175b^{t}[/tex]

Half-life of 122 days.

This means that [tex]M(122) = 0.5*175 = 87.5[/tex]

So

[tex]M(t) = 175b^{t}[/tex]

[tex]87.5 = 175b^{122}[/tex]

[tex]b^{122} = 0.5[/tex]

[tex]\sqrt[122]{b^{122}} = \sqrt[122]{0.5}[/tex]

[tex]b = 0.9943[/tex]

So

[tex]M(t) = 175(0.9943)^{t}[/tex]

Answer:

There are 200 4th grades and 360 third graders

Step-by-step explanation:

560/2=280-80=200 280+80=360

Answer:

It would be 18;24 or simplified it would be 3;4

Step-by-step explanation:

24-6=18 so there are 18 role playing games. So the ratio could be 18;24 but if it needs to be simplified you can divide both numbers by 6. 18/6=3 and 24/6=4

Answer:

Area of the StarKist label around the can in terms of π = 12π cm²

Step-by-step explanation:

Given;

the volume of a can of StarKist tuna, V = 18 π cm³

height of the can of StarKist tuna, h =  2 cm

To determine the area of the StarKist label that wraps around the entire can and does not overlap, we assume the can to have a shape of a cylinder.

Volume of the can = πr²h

where;

r is radius of the can

h is height of the can

πr² x 2 = 18 π

2r² = 18

r² = 18/2

r² = 9

r = 3

Area around the can = curved surface area of the can (cylinder)

Curved surface area of the can = 2πr × h = 2πrh

Curved surface area of the can = 2πrh = 2π x 3 x 2 = 12π cm²

Area of the StarKist label around the can in terms of π = 12π cm²

Answer:

I think +5 or 5

Answer:

there both 5

Step-by-step explanation: did the question on edg