Kaylee has $4,500 for a down payment and thinks she can afford monthly payments of $300. If he can finance a vehicle with a 7%, 4-year loan (assume a 0% tax rate), what is the maximum amount Kaylee can afford to spend on the car? [use the calculation in the text or the online calculators in the resource section]

Answer:

8π cm^2

Step-by-step explanation:

We proceed as follows;

To answer this question, what we need firstly is the name of the cross section that results from slicing a sphere into half.

The cross section that results is called a hemisphere, which is half the size of the sphere.

But before we can calculate the area of the new cross section, we will need the radius of the original shape.

This is obtainable from the volume of the shape.

Mathematically;

Volume of a sphere = 4/3 * π * r^3

32/3 * π = 4/3 * π * r^3

We can take off π/3 from both sides so we are left with;

32 = 4r^3

Divide through by 4

r^3 = 8

r is the cube root of 8 = 2 cm

Now we find the area of the hemisphere

Mathematically, the area of a hemisphere is 2 * π * r^2

using the value of r = 2 cm given above, we have Hemisphere area = 2 * π * 2^2 =8 π cm^2

Answer:

β = (-0.19 dB).

Step-by-step explanation:

The formula which is used to calculate the decibel level of a sound is given by :

[tex]\beta=10\log (\dfrac{I}{I_o})[/tex]

I is intensity of the sound of a ticking clock

[tex]I_o=10^{-12}\[/tex] watts per square meter

Since, [tex]1\ \text{inch}^2=\dfrac{1}{1550}\ \text{m}^2[/tex]

The intensity of a monster truck is converted into per square meter as follows:  

[tex]10^{-9}\ {W/in^2}= \dfrac{10^{-9}}{1550}\ W/m^2\\\\10^{-9}\ {W/in^2}=6.45\times 10^{-13}\ W/m^2[/tex]

So, Decibal level is :

[tex]\beta=10\log (\dfrac{6.45\times 10^{-13}}{10^{-12}})\\\\\beta =-0.19\ dB[/tex]

So, the decibel level of the sound of a ticking clock is (-0.19 dB).

Answer:

30dB

Step-by-step explanation:

Answer:

Option D is the correct option.

Step-by-step explanation:

Given,

A ( 4, 5 ) , B ( 2 , 2 ) , C ( 4 , 2 )

Let,

A ( 4 , 5 ) → ( x1 , y1 )

B ( 2 , 2 ) → ( x2 , y2 )

Now, finding the length of AB

Use the distance formula to find the length of AB

[tex] = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]

plug the values

[tex] = \sqrt{ {(2 - 4)}^{2} + {(2 - 5)}^{2} } [/tex]

Calculate the difference

[tex] = \sqrt{ {( - 2)}^{2} + {( - 3)}^{2} } [/tex]

Evaluate the power

[tex] = \sqrt{4 + 9} [/tex]

Add the numbers

[tex] = \sqrt{13} [/tex]

Hope this helps..

Best regards!!

Answer:

we reject  H₀

Step-by-step explanation:  Se annex

The test is one tail-test (greater than)

Using   α = 0,05   (critical value )  from z- table we get

z(c) = 1,64

And Test hypothesis is:

H₀         Null hypothesis           μ   =  μ₀

Hₐ       Alternate hypothesis   μ   >  μ₀

Which we need to compare with z(s) = 2,19  (from problem statement)

The annex shows z(c), z(s), rejection and acceptance regions, and as we can see z(s) > z(c) and it is in the rejection region

So base on our drawing we will reject  H₀

Answer:

n × 0.77

Step-by-step explanation:

Decreasing a number by 23% is the same as multiplying that number by 0.77, so n number of animals decreased by 23% is:

n × 0.77

Answer:

[tex] g(x) =\sqrt{x-4}[/tex]

[tex] h(x) =2x-8[/tex]

And we want to find:

[tex] g o h(x)[/tex]

Replacing we got:

[tex] go h(x)= \sqrt{2x-8 -4}= \sqrt{2x-12}[/tex]

And the restriction for this case would be:

[tex] 2x-12 \geq 0[/tex]

[tex] 2x \geq 12[/tex]

[tex] x \geq 6[/tex]

Step-by-step explanation:

Assumign that we have the following two functions:

[tex] g(x) =\sqrt{x-4}[/tex]

[tex] h(x) =2x-8[/tex]

And we want to find:

[tex] g o h(x)[/tex]

Replacing we got:

[tex] go h(x)= \sqrt{2x-8 -4}= \sqrt{2x-12}[/tex]

And the restriction for this case would be:

[tex] 2x-12 \geq 0[/tex]

[tex] 2x \geq 12[/tex]

[tex] x \geq 6[/tex]

Answer:

the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4%  is 0.0042

Step-by-step explanation:

Given that :

A film distribution manager calculates that 9% of the films released are flops

Let p be the probability for the movies that were released are flops;

[tex]\mu_p = P = 0.9[/tex]

If the manager is right, what is the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4%

now; we know that our sample size = 442

the standard deviation of the variance  is [tex]\sigma_p= \sqrt{\dfrac{p(1-p)}{n}}[/tex]

[tex]\sigma_p= \sqrt{\dfrac{0.9(1-0.9)}{442}}[/tex]

[tex]\sigma_p= \sqrt{\dfrac{0.9(0.1)}{442}}[/tex]

[tex]\sigma_p= \sqrt{\dfrac{0.09}{442}}[/tex]

[tex]\sigma_p= \sqrt{2.0361991 \times 10^{-4}}[/tex]

[tex]\sigma _p = 0.014[/tex]

So; if the manager is right; the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4% can be calculated as:

[tex]P(|p-P|>0.04)=1 -P(p-P|<0.04)[/tex]

[tex]P(|p-P|>0.04)=1 -P(-0.04 \leq p-P \leq 0.04)[/tex]

[tex]P(|p-P|>0.04)=1 -P( \dfrac{-0.04}{\sigma_p} \leq \dfrac{ p-P}{\sigma_p} \leq \dfrac{0.04}{\sigma_p})[/tex]

[tex]P(|p-P|>0.04)=1 -P( \dfrac{-0.04}{0.014} \leq Z\leq \dfrac{0.04}{0.014})[/tex]

[tex]P(|p-P|>0.04)=1 -P( -2.8571 \leq Z\leq 2.8571)[/tex]

[tex]P(|p-P|>0.04)=1 -[P(Z \leq 2.8571) -P (Z\leq -2.8571)[/tex]

[tex]P(|p-P|>0.04)=1 -(0.9979 -0.0021)[/tex]

[tex]P(|p-P|>0.04)=1 -0.9958[/tex]

[tex]\mathbf{P(|p-P|>0.04)=0.0042}[/tex]

∴

the probability that the proportion of flops in a sample of 442 released films would differ from the population proportion by greater than 4%  is 0.0042

Answer:

the grade point average​ (GPA) of the student is 2.27

If the​ Dean's list requires a GPA of 3.00 or​ greater,  the student did not make the Dean's list.

Step-by-step explanation:

Given that:

A student grade are as follows:

B    ---   3

F   ---   0

B   ----   3

B  ----- 3

C ------- 2

Those courses had the corresponding numbers of credit hours 4​, 2​, 1​, 2​, and 2.

The grading system assigns quality points to letter grades as​ follows:

A = 4; B=​3; C=​2; D=​1; F=0

The sample mean simply implies the sum of the products of the value and the weights divided by the total weights;

i.e

[tex]\overline x = \dfrac{\sum xf}{n }[/tex]

[tex]\overline x = \dfrac{3(4)+0(2)+3(1)+3(2)+2(2)}{4+2+1+2+2 }[/tex]

[tex]\overline x = \dfrac{12+0+3+6+4}{11 }[/tex]

[tex]\overline x = \dfrac{25}{11 }[/tex]

[tex]\overline x =[/tex] 2.27

the grade point average​ (GPA) of the student is 2.27

If the​ Dean's list requires a GPA of 3.00 or​ greater,  the student did not make the Dean's list.

Answer:

The amount of CD's she could buy would be 3.

Step-by-step explanation:

80-20=60

60÷18 = 3 CD's

Answer:

1,2,3

Step-by-step explanation:

Answer:

1992.50 mL; 825 mL

Step-by-step explanation:

Given that :

Capacity of bottles in the attachment = 2L

Amount of soft drink in bottle 1 = 7.50mL

Amount of soft drink in bottle 2 = 1175mL

Converting liter milliliter

1Litre = 1000 milliliters

Therefore 2Litres = 2000 milliliters

Capacity each of bottle = 2000 milliliters

Volume of drink required to completely fill bottle 1:

2000mL - 7.50mL = 1992.50 mL

Volume of drink required to completely fill bottle 2:

2000mL - 1175mL = 825 mL

Your question has been heard loud and clear.

Answer is option d or the fourth option.

thank you

Answer:

LN and NK

Step-by-step explanation:

trust

Answer: c

Step-by-step explanation:

Its correct

Answer:

1.35 degrees per mg.

Step-by-step explanation:

The patient's temperature went from 105.85 to 99.1. That is a decrease of 6.75 degrees. You want to find the temperature decrease per milligram, which can be found by dividing the temperature by the number of mg of the drug.

6.75 / 5 = 675 / 500 = 1.35

So, the rate at which her temperature decreased per milligram is 1.35 degrees per mg.

Hope this helps!

I believe it is C, as the graphs do look the same.

Answer:

Add the equations to eliminate x.  

Step-by-step explanation:

(1)  y = 10 + x

(2) y =   3 - x

An easy way to solve this problem is to add the two equations to eliminate x.

(3) 2y = 13

From here, you can calculate y and then x.

Answer:

9/4n= 1.5/7

right now to find this equation it is a proportion so you cross multiply and you gonna get 63=6n and divide 6 on both sides and u get 10.5.

Check 9/4n= 9/42 and to simply u will get 1.5/7

Step-by-step explanation:

Answer:

1a (x + y)² = x² + 2xy + y²

1b. (x - y)² = x² - 2xy + y²

2. (x + y)² - (x - y)² = 4xy

3. 4² – 2² = 12

Step-by-step explanation:

1a. Expansion of (x + y)²

(x + y)² = (x + y)(x + y)

(x + y)² = x(x + y) + y(x + y)

(x + y)² = x² + xy + xy + y²

(x + y)² = x² + 2xy + y²

1b. Expansion of (x - y)²

(x - y)² = (x - y)(x - y)

(x - y)² = x(x - y) - y(x - y)

(x - y)² = x² - xy - xy + y²

(x - y)² = x² - 2xy + y²

2. Determination of (x + y)² - (x - y)²

This can be obtained as follow

(x + y)² = x² + 2xy + y²

(x - y)² = x² - 2xy + y²

(x + y)² - (x - y)² = x² + 2xy + y² - (x² - 2xy + y²)

= x² + 2xy + y² - x² + 2xy - y²

= x² - x² + 2xy + 2xy + y² - y²

= 2xy + 2xy

= 4xy

(x + y)² - (x - y)² = 4xy

3. Writing 12 as the difference of two perfect square.

To do this, we shall subtract 12 from a perfect square to obtain a number which has a perfect square root.

We'll begin by 4

4² – 12

16 – 12 = 4

Find the square root of 4

√4 = 2

4 has a square root of 2.

Thus,

4² – 12 = 4

4² – 12 = 2²

Rearrange

4² – 2² = 12

Therefore, 12 as a difference of two perfect square is 4² – 2²

Explanation:

The outer term 2p is distributed among the three terms inside the parenthesis. We will multiply 2p by each term inside

2p times 4p^2 = 2*4*p*p^2 = 8p^3

2p times 5p = 2*5*p*p = 10p^2

2p times 7 = 2*7p = 14p

The results 8p^3, 10p^2 and 14p are added up to get the final answer shown above. We do not have any like terms to combine, so we leave it as is.

Answer: 50 degrees

Step-by-step explanation:

180-85=95

180-145=35

interior angle sum for a triangle is 180 degrees, so 180=95+35+a

m of angle A is 50 degrees

Answer:

Area of the triangle WXY = 111.8 mm²

Step-by-step explanation:

By applying Sine rule in the given triangle WXY,

[tex]\frac{\text{SinW}}{\text{XY}}=\frac{\text{SinX}}{\text{WY}}=\frac{\text{SinY}}{\text{WX}}[/tex]

Since m∠W + m∠X + m∠Y = 180°

m∠W + 26° + 130° = 180°

m∠W = 180° - 156°

m∠W = 24°

[tex]\frac{\text{Sin24}}{\text{XY}}=\frac{\text{Sin130}}{31}=\frac{\text{Sin26}}{\text{WX}}[/tex]

[tex]\frac{\text{Sin24}}{\text{XY}}=\frac{\text{Sin130}}{31}[/tex]

XY = [tex]\frac{31\times (\text{Sin24})}{\text{Sin130}}[/tex]

XY = 16.4597

     ≈ 16.4597 mm

Area of the triangle = [tex]\frac{1}{2}(\text{XY})(\text{WY})\text{SinY}[/tex]

                                 = [tex]\frac{1}{2}(16.4597)(31)\text{Sin26}[/tex]

                                 = 111.83 mm²

                                 ≈ 111.8 mm²

Therefore, area of the triangle WXY = 111.8 mm²

Answer:

17.3 = AC

Step-by-step explanation:

Since this is a right angle, we can use trig functions

tan B = opp/ adj

Tan 68 = AC / 7

7 tan 68 = AC

17.32560797 = AC

To 1 decimal place

17.3 = AC

Answer:

Step-by-step explanation:

To find AC we use tan

tan ∅ = opposite / adjacent

From the question

AB is the adjacent

AC is the opposite

So we have

tan 68 = AC / AB

AC = AB tan 68

AC = 7 tan 68

AC = 17.32

AC = 17. 3 cm to one decimal place

Hope this helps you

Answer:

1/16.4616

Step-by-step explanation:

(1.9^2*2.4^-3) (1.9^3*2.4^-2)^-3

(1.9^2*2.4^-3) * 1 / (1.9^3*2.4^-2)^3

1.9^2*2.4^-3 / (1.9^3*2.4^-2)^3

1.9^2 * 1 / 2.4^3 ÷ (1.9^3* 1 / 2.4^2)3

1.9^2 / 2.4^3 × (2.4^2/1.9^3)^3

(1/2.4) (1/1.9)^3

(1/2.4) (1/6.859)

1/16.4616

Answer:

[tex]\Large \boxed{\sf\ \ (0,-9) \ \ }[/tex]

Step-by-step explanation:

Hello,

We know that when the parabola equation is

   [tex]y=a(x-h)^2+k[/tex]

the vertex is (h,k) and the focus is

   [tex](h,k+\dfrac{1}{4a})[/tex]

Here, the equation is

   [tex]y=-\dfrac{1}{12}x^2-6[/tex]

so

   [tex]a=-\dfrac{1}{12}\\\\h = 0\\\\k =-6[/tex]

So,

[tex]k+\dfrac{1}{4a}=-6-\dfrac{12}{4}=-6-3=-9[/tex]

Then, the focus is

[tex]\large \boxed{\sf\ \ (0,-9) \ \ }[/tex]

I attached the graph, included the focus so that you can see it :-)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

So possibilities of zeroes are:

Positive       Negative       Imaginary

   1                    1                   2

   3                   1                   0

Zeroes = -1.4549, 1.2658, 0.34457-1.0503i, 0.34457+1.0503i.  

Step-by-step explanation:

Note: Descartes' Rule of Signs is used to find the signs of zeroes not the exact value.

The given function is

[tex]f(x)=4x^4-2x^3-3x^2+6x-9[/tex]

Degree of polynomial is 4 so number of zeroes is 4.

There are three sign changes, so there are either 3 positive zeros or 1 positive zero.

Now, put x=-x in f(x).

[tex]f(-x)=4(-x)^4-2(-x)^3-3(-x)^2+6(-x)-9[/tex]

[tex]f(-x)=4x^4+2x^3-3x^2-6x-9[/tex]

There is one variation in sign change, so there is 1 negative zero.

So possibilities of zeroes are:

Positive       Negative       Imaginary

   1                    1                   2

   3                   1                   0

Using graphing calculator the zeroes of given function are -1.4549, 1.2658, 0.34457-1.0503i and 0.34457+1.0503i.  

Answer:

median

Step-by-step explanation:

(median is used to measure the middle)

you just line up all the numbers from least to greatest, then pick the middle number, IF there are NO numbers in the middle, you add the the 2 middle numbers up, then divided by 2

Answer:

Median, because there is 1 outlier that affects the center

Step-by-step explanation:

"The median is the middle number of the data set. It is exactly like it sounds. To figure out the median you put all the numbers in order (highest to lowest or lowest to highest) and then pick the middle number. If there is an odd number of data points, then you will have just one middle number."

Answer: x Less-than-or-equal-to 2.25

Step-by-step explanation:

The given inequality: 47.75 + x Less-than-or-equal-to 50.

To determine: How much more weight can be added to Li’s suitcase without going over the 50-pound limit.

i.e. inequality for x.

[tex]47.75+x\leq50[/tex]

Subtract 47.75 from both the sides, we get

[tex]x\leq50-47.75\\\\\Rightarrow\ x\leq2.25[/tex]

So, the solution set is "x Less-than-or-equal-to 2.25"

Hence, the correct answer is "x Less-than-or-equal-to 2.25."

Answer

A x <_ 2.25

Step-by-step explanation:

Answer:

B) 5 + 3√5 units

Step-by-step explanation:

The length of ZX is 2√5 units. What is the perimeter of triangle XYZ?  

A) 5 +√3 + 2 √5 units  

B) 5 + 3√5 units  

C) 5 + √6 + 2√5 units  

D) 10 + 2√5 units

From the diagram attached, point X is at (-1, 4), Y(3, 1), Z(1, 0).

The distance between two point

[tex]O(x_1,y_1)\ and\ A(x_2,y_2)\ is\ given\ as:\\\\OA=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

The lengths of the sides of the triangle are:

[tex]|XY| = \sqrt{(3-(-1))^2+(1-4)^2}=\sqrt{25} =5\ unit\\ \\|XZ|= \sqrt{(1-(-1))^2+(0-4)^2}=\sqrt{20} =2\sqrt{5} \ unit\\\\|YZ|= \sqrt{(1-3)^2+(0-1)^2}=\sqrt{5} \ unit[/tex]

The perimeter of the triangle is the sum of all the sides, i.e.

Perimeter = |XY| + |YZ| + |XZ| = 5 + 2√5 + √5 = 5 + 3√5  

Answer:

B

Step-by-step explanation:

Answer:

[tex]b = 74\ cm[/tex]

Step-by-step explanation:

The volume of a prism is given by the following equation:

[tex]Volume = base\ area * height[/tex]

In our case, the base is a triangle, so the area is given by:

[tex]base\ area = base * height_{\Delta}/2[/tex]

The base of the triangle is 43 cm, the height of the triangle is b, the height of the prism is 24 and the volume of the prism is 38,184, so we have:

[tex]base\ area = 43 * b/2 = 21.5b[/tex]

[tex]38184 = 21.5b * 24[/tex]

[tex]b = 38184/(24*21.5)[/tex]

[tex]b = 74\ cm[/tex]

Answer:

3/2

Step-by-step explanation:

● (-3/8) ÷(-1/4)

Flip the second fraction by putting 1 instead 4 and vice versa.

● (-3/8)* (-4/1)

-4 over 1 is -4 since dividing by 1 gives the same number.

● (-3/8)*(-4)

Eliminate the - signs in both fractions since multiplying two negative numbers by each other gives a positive number.

●( 3/8)*4

● (3*4/8)

8 is 2 times 4

● (3*4)/(4*2)

Simplify by eliminating 4 in the fraction.

● 3/2

The result is 3/2

Answer:

7.1 km

Step-by-step explanation:

Bien, este es un problema de conversión de unidades.

Procedemos de la siguiente manera;

Convirtamos todas las alturas que tenemos a metros.

Comenzamos con 23,000 decímetros a metros Matemáticamente, 1 metro = 10 decímetros Entonces 23,000 decímetros = 23,000 / 10 = 2,300 metros

En segundo lugar, convertimos 54 hectómetros a metros.

Matemáticamente; 1 hectómetro = 100 metros Entonces 54 hectómetros = 54 * 100 = 5400 metros Por lo tanto, su nueva altura sería; 14,800-2300-5400 = 7,100 metros Ahora, procedemos a convertir 7.100 metros a kilómetros.

Matemáticamente 1000 m = 1 km Entonces 7,100 m serán = 7100/1000 = 7.1 km

Responder:

Explicación paso a paso:

Altura inicial del avión = 14.800 m.

Como se redujo en 23,000 decímetros y luego en 54 hectómetros, la caída total de altura se obtiene al agregar 23,000 decímetros y 54 hectómetros

Antes de agregarlos, necesitamos convertir ambos valores a metros

1 decímetro = 0.1m

23,000 decímetros = x

x = 23,000 * 0.1

x = 2,300 metros

Además, si 1 hectómetro = 100 m

54 hectómetros = y

y = 54 * 100

y = 5400 metros.

Sumando ambas alturas;

x + y = 2300m + 5400m = 7700 metros

Esto significa que el avión cae por una altura total de 7700 metros

Para calcular la altura a la que volará el avión después de la caída, tomaremos la diferencia entre la altura inicial y la altura total caída.

La altura que el avión está volando ahora será 14,800 - 7,700 = 7,100 metros

Convirtiendo la respuesta final a kilómetros.

1000m = 1km

7.100m = z

z = 7100/1000

z = 7.1 km

Esto significa que el avión está volando a una altura de 7.1 kilómetros después de la caída.