Write an equation in slope-intercept form for the line that passes through (8,1) and (4,3).

The probability that an item is either Large or Blue, [tex]\( P(\text{Large or Blue}) \)[/tex], is 0.7 after simplification.

To find the probability [tex]\( P(\text{Large or Blue}) \)[/tex], we will use the principle of inclusion-exclusion. The formula for two events A and B is:

[tex]\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \][/tex]

Let's define our events as:

- A = The event that an item is Large.

- B = The event that an item is Blue.

Looking at the table:

- The probability that an item is Large, [tex]\( P(\text{Large}) \)[/tex], is the sum of all Large items divided by the total number of items.

- The probability that an item is Blue, [tex]\( P(\text{Blue}) \)[/tex], is the sum of all Blue items divided by the total number of items.

- The probability that an item is both Large and Blue, [tex]\( P(\text{Large and Blue}) \)[/tex], is the number of items that are both Large and Blue divided by the total number of items.

From the table:

Now we can calculate the probabilities:

[tex]\[ P(\text{Large}) = \frac{25}{40} \][/tex]

[tex]\[ P(\text{Blue}) = \frac{20}{40} \][/tex]

[tex]\[ P(\text{Large and Blue}) = \frac{17}{40} \][/tex]

Using the inclusion-exclusion principle:

[tex]\[ P(\text{Large or Blue}) = P(\text{Large}) + P(\text{Blue}) - P(\text{Large and Blue}) \][/tex]

Let's do the calculations.

The probability of an item being Large or Blue is [tex]\( P(\text{Large or Blue}) = 0.7 \)[/tex], which is already in its simplest form.

Answer:

72,000

Step-by-step explanation:

wth dude i do not know

Answer:

x =16

Step-by-step explanation:

You can use Theorem Pythagoras method to solve this question.

The formula is a^2 + b^2 =c^2

In this question a=x , b=12, and c= 20

to find a which means x you should use this formula : c^2 - b^2=20^2-12^2

= 400 - 144

=√256

=16

You also can use another method by using the second diagram.

In that diagram you have to know that 12÷3 is 4, 20÷5 is 4, hence x÷4 is 4

so , x=16.

I hope this two ways for answering this question will be helpful for you.

Answer:

x = 16

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{x}{4}[/tex] = [tex]\frac{20}{5}[/tex] ( cross- multiply )

5x = 4 × 20 = 80 ( divide both sides by 5 )

x = 16

Answer:  B) 1.6

Step-by-step explanation:

[tex]P=100e^{0.70t}\\\\\underline{\text{Substitute P = 300:}}\\300=100e^{0.70t}\\\\\\\underline{\text{Divide both sides by 100:}}\\3=e^{0.70t}\\\\\\\underline{\text{Apply ln to both sides:}}\\ln\ 3=ln\ e^{0.70t}\\\\\\\underline{\text{ln e cancels out:}}\\ln\ 3=0.70t\\\\\\\underline{\text{Divide both sides by 0.70:}}\\\dfrac{ln\ 3}{0.70}=t\\\\\\\underline{\text{Evaluate using a calculator:}}\\1.569=t[/tex]

Answer:

B

Step-by-step explanation:

Use the law of sines to create a proportion.

[tex]\frac{18}{sin(90)}=\frac{x}{sin(20)}[/tex]

Solve for [tex]x[/tex].

[tex]x=6.2[/tex]

Answer:

[tex]x=6.2[/tex]

Step-by-step explanation:

Given triangle is right triangle so we can use trigonometric ratios to find the value of x.

[tex]\sin\left(\theta\right)=\frac{opposite}{hypotenuse}[/tex]

[tex]\sin\left(20^o\right)=\frac{x}{18}[/tex]

[tex]\sin\left(20^o\right)(18)=x[/tex]

[tex](0.34202014332566873304409961468226)(18)=x[/tex]

[tex]6.1563625798620371947937930642807=x[/tex]

[tex]x=6.1563625798620371947937930642807[/tex]

[tex]x=6.2[/tex]

Hence final answer is [tex]x=6.2[/tex]

Answer:

The fraction will decrease [tex]33.33\%[/tex]

Step-by-step explanation:

Let

x/y ----> the fraction

we know that

100%-50^=50%=50/100=0.50

100%-25%=75%=75/100=0.75

substitute

[tex]\frac{x}{y}*\frac{0.50}{0.75} =\frac{2}{3}(\frac{x}{y})[/tex]

therefore

The percent that the fraction will decrease is equal to

[tex](1-\frac{2}{3})*100=33.33\%[/tex]

ANSWER

9.6

EXPLANATION

The given trigonometric equation is:

[tex] \cos(21 \degree) = \frac{9}{y} [/tex]

We want to find y, so we multiply both sides by y to get,

[tex]y\cos(21 \degree) = \frac{9}{y} \times y[/tex]

Cancel out the common factors,

.

[tex]y\cos(21 \degree) = 9[/tex]

. Divide both sides by cos(21°)

[tex]y= \frac{9}{\cos(21 \degree)} [/tex]

[tex]y = 9.64[/tex]

To the nearest tenth, y=9.6

Answer:

y = ln( x + 6 ) - 11

h = 6

k = -11

h + k = -5

Step-by-step explanation:

Horizontal shift changes whats inside the brackets, in other words, changes just the x-value.If the shift is right, the number should be subtracted, if the shift is left, the number should be added.

Vertical shift changes the equation as a whole.if the shift is up, the number of should be added.If the shift is down, the number should be subtracted.

The changes given to us are 3 units left ( horizontal translation ) and 5 units down ( vertical translation )

If we rewrite the equation, we have:

y = ln( x + 3 + 3 ) - 6 - 5

y = ln( x + 6 ) - 11

Answer:

25 ft

Step-by-step explanation:

The tree's shadow is 4 times the length of the man's shadow, so we presume the tree is 4 times the height of the man: 4 × (6 ft 3 in) = (24 ft 12 in) = 25 ft.

Answer:

13

Step-by-step explanation:

You need to use the Pythagorean theorem. Which is a^2+b^2=c^2

so 5^2+12^2

which simplifies to 25+144=c^2

then it simplifies to 169=c^2

Now you take the square root

c=sqrt(169)

c=13

For this case we have that by definition, the Pythagorean theorem states that:

[tex]c = \sqrt {a ^ 2 + b ^ 2}[/tex]

Where:

c: It is the hypotenuse

a, b: Are the legs

Substituting the values of the figure:

[tex]c = \sqrt {5 ^ 2 + 12 ^ 2}\\c = \sqrt {25 + 144}\\c = \sqrt {169}\\c = 13[/tex]

Thus, the value of the hypotenuse is 13.

Answer:

13

Option B

Answer:

what

Step-by-step explanation:

Answer:

B. greater mean = class B greater median = class B

Step-by-step explanation:

Answer:

64/3 cc or 64/3 cm³

Step-by-step explanation:

The formula for the volume of a triangular pyramid is

V = (1/3)(area of base)(height)

Here we have a square prism (actually, a cube), whose square base is 4 cm by 4 cm (4 cm is the cube root of 64 cc).  The height of this cube is also 4 cm.

The volume of a triangular pyramid of base area (4 cm)² and height 4 cm is

V = (1/3)(base area)(height)

   = (1/3)(16 cm²)(4 cm) = 64/3 cc

Answer:

64/3 cc or 64/3 cm³

Step-by-step explanation:

Answer:

The size of Harry's loan is $9000.

Step-by-step explanation:

D(t) models Harry's remaining debt, in dollars, as a function of time t, in months  that is given by :

[tex]D(t) =-200t+ 9000[/tex]

We can see 200 is in negative that means it is getting deducted from the function. So, Harry must be paying this each month against his loan.

Lets put t = 0, that shows no payments have been made.

This will get the amount of loan, before any payments.

[tex]D(t)=-200(0)+9000[/tex]

So,[tex]D(t) =9000[/tex]

Hence, the size of Harry's loan is $9000.

Answer:

$200

Step-by-step explanation:

I got $9000 wrong on Khan and $200 right

The 21 compartments will be fully filled and the last compartment will contain 3 towels.

The number of compartments that will be filled =  total number of towels/ capacity of one compartment.

So we have 150 towels / 7 towels per compartment ≈ 21.43.

Since we can't have a fraction of a compartment, this means that 21 compartments will be fully filled.

The remaining towels can be found = the total number of towels - the number of towels that fit into the full compartments

Total no. of towels that fit into all compartments = 21 compartments × 7 towels each = 147 towels.

Therefore, we have 150 - 147 = 3 towels left, which will be in the compartment that is not completely filled.

There are 21 compartments filled with towels, and in the 22nd compartment, there will be 3 towels.

Number of compartments filled: 21 compartments  

Towels in a partially filled compartment: 6 towels  

To calculate the number of compartments filled, we need to divide the total number of towels by the maximum number of towels each compartment can hold:

[tex]\( \text{Number of compartments filled} = \frac{\text{Total number of towels}}{\text{Maximum towels per compartment}} \)[/tex]

[tex]\( \text{Number of compartments filled} = \frac{150}{7} = 21.4285 \)[/tex]

Since we can't have a fraction of a compartment, we round down to the nearest whole number, which is 21.

To find out how many towels will be in a compartment that is not completely filled, we subtract the total number of towels already placed in filled compartments from the total number of towels:

[tex]\( \text{Remaining towels} = \text{Total number of towels} - (\text{Number of compartments filled} \times \text{Maximum towels per compartment}) \)[/tex]

[tex]\( \text{Remaining towels} = 150 - (21 \times 7) = 150 - 147 = 3 \)[/tex]

So, there are 21 compartments filled with towels, and in the 22nd compartment, there will be 3 towels.

Complete question

A storage compartment for a gym locker room can hold up to 7 folded towels. There are 22 compartments for towels. Katie has 150 towels to fold and put away. How many of the compartments will be filled? How many towels will be in a compartment that is not completely filled?

Answer:

  sphere, cylinder, (right circular) cone

Step-by-step explanation:

Any cross section of a sphere is a circle.

A cross section parallel to the base of a cylinder or cone will have the same shape as the base. By definition, a cylinder has a circular base. A "right circular" cone will also have a circular base.

___

A torus, ellipsoid, or hyperboloid may also have a circular cross section.

See attachment for solution steps and answer.

The slope of the line through the points (-1,6) and (7,-2) is -1. Substitute this and one of the points into the point-slope form, 'y - y1 = m (x - x1)', to get the equation of the line. The final equation is y = -x + 5.

To complete the equation of the line through points (-1,6) and (7,-2), we first need to find the slope (m) of the line using the formula m=(y2-y1)/(x2-x1). Here, (-1,6) is (x1,y1) and (7,-2) is (x2,y2). When we substitute these values in, we get m=(-2-6)/(7-(-1)), which simplifies to m=-8/8 or m=-1.

Now, you can use the point-slope form of a line, which is y - y1 = m (x - x1). You can use either of the points given, but let's use (-1,6). The equation then becomes y - 6 = -1(x - (-1)). To simplify, this becomes y - 6 = -x - 1. If you add 6 to both sides, the final equation of the line is y = -x + 5.

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I am pretty sure it’s step one

Answer:

The correct choice is C

Step-by-step explanation:

The given curve is described by the parametric equations:

[tex]x=4-t[/tex]

[tex]y=t^2-2[/tex]

Let us eliminate the parameter by making t the subject in the first equation and substitute into the second equation;

[tex]t=4-x[/tex]

We substitute this into the second equation to get:

[tex]y=(4-x)^2-2[/tex]

This is the equation of a parabola whose vertex is at (4,-2)

The correct choice is C

The volume of the foam is  : 8[tex]r^{3}[/tex]

A cube is a three dimensional shape made of 6 squares.

it has 8 corners and 12 edges.

Analysis:

Given that the sphere fits snugly in the cube the length of each face of the cube would be twice the radius of the sphere.

therefore:

L = 2r

where r = radius of sphere,

L = length of each face of cubic foam

volume of cubic foam = [tex]L^{3}[/tex]

= [tex](2r)^{3}[/tex]

= [tex]8r^{3}[/tex]

In conclusion, the volume of the cubic foam is  [tex]8r^{3}[/tex]

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Answer:

yes; 5

Step-by-step explanation:

To determine if the sequence is arithmetic, take the second term and subtract the first term

-7 - (-12) = -7+12 = 5

This would be the common difference if our sequence is arithmetic

Now take the second term and add the"common difference"

-7+5 = -2  This is our third term

-2+5 = 3  This is our fourth term

The sequence is arithmetic with a common difference of 5

Answer:

  a) 708.00

  b) 108.00

  c) 11

Step-by-step explanation:

a) The cost is $59 for each of 12 months, so the total cost is ...

  12×$59 = $708

__

b) The "carrying charges" are the difference between what is paid and the cash price:

 $708 -600 = $108

__

c) Saving at the rate of $59 per month, it will take ...

  $600/($59/mo) ≈ 10.17 mo

to save the money. The amount saved will be $590, or $10 short of the required amount after 10 months, so it will take 11 months to save enough for the cash purchase.

Answer:

 a) 708.00

 b) 108.00

 c) 11

Step-by-step explanation:

Answer:

The measure of angle JKL is m∠JKL=35°

Step-by-step explanation:

step 1

Find the measure of the arc KL

we know that

arc KL+arc KN+arc NL=360° ----> by complete circle

arc KL+150°+140°=360°

arc KL=360°-290°=70°

step 2

Find the measure of angle JKL

we know that

The inscribed angle is half that of the arc it comprises.

so

m∠JKL=(1/2)[arc KL]

substitute

m∠JKL=(1/2)[70°]=35°

Percent error = |(Measured - Actual) / Actual| × 100. For Measured 68, Actual 60: [tex]\( \frac{|68 - 60|}{60} \times 100 ≈ 13.3\% \).[/tex]

To find the percent error, you can use the formula:

[tex]\[ \text{Percent Error} = \left| \frac{\text{Measured Value} - \text{Actual Value}}{\text{Actual Value}} \right| \times 100 \]\\[/tex]

Given:

- Measured Value = 68

- Actual Value = 60

Substitute these values into the formula:

[tex]\[ \text{Percent Error} = \left| \frac{68 - 60}{60} \right| \times 100 \]\[ \text{Percent Error} = \left| \frac{8}{60} \right| \times 100 \]\[ \text{Percent Error} = \left| 0.1333... \right| \times 100 \]Now, rounding to the nearest tenth:\[ \text{Percent Error} ≈ 13.3\% \]\\[/tex]

So, the percent error is about 13.3%. This indicates that the measured value is approximately 13.3% higher than the actual value.

The percent error, rounded to the nearest tenth, is about 13.3%.

To find the percent error, you can use the following formula:

[tex]\[\text{Percent Error} = \frac{{|\text{Estimated Value} - \text{Actual Value}|}}{{\text{Actual Value}}} \times 100.\][/tex]

Here, the estimated value is 68 marbles, and the actual value is 60 marbles.

Calculate the absolute error :

  [tex]\[ |\text{68 - 60}| = 8. \][/tex]

Calculate the relative error :

[tex]\[ \frac{{8}}{{60}}. \][/tex]

Convert to percentage :

[tex]\[ \frac{{8}}{{60}} \times 100 = 13.333. \][/tex]

Round to the nearest tenth :

[tex]\[ \approx 13.3.[/tex]

Thus, the percent error, rounded to the nearest tenth, is about 13.3%.

Question :

You estimate that a jar contains 68 marbles. The actual number of marbles is 60. Find the percent error. Round your answer to the nearest tenth. The percent error is about %.

Answer:

3a5b

Step-by-step explanation:

Answer:

3a5b

Step-by-step explanation:

Answer:

(D)[tex]x=104^{\circ}[/tex]

Step-by-step explanation:

Given: It is given that circle O is circumscribed about quadrilateral ABCD such that ∠ABC=91° and ∠ADC=x-15°.

To find: the value of x.

Solution: It is given that circle O is circumscribed about quadrilateral ABCD such that ∠ABC=91° and ∠ADC=x-15°.

We know that the sum of opposite angles of the cyclic quadrilateral is 180°, therefore

[tex]{\angle}ABC+{\angle}ADC=180^{\circ}[/tex]

Substituting the given values, we have

[tex]91^{\circ}+x-15^{\circ}=180^{\circ}[/tex]

[tex]x+76^{\circ}=180^{\circ}[/tex]

[tex]x=104^{\circ}[/tex]

thus, the value of x is [tex]104^{\circ}[/tex].

Hence, option D is correct.

Answer:

the answer is 104 i just took quiz 6.11.3

Step-by-step explanation:

Answer:

(2x8 - 3y2) • (4x16 + 6x8y2 + 9y4)

Step-by-step explanation:

For this case we must factor the following expression:

[tex]8x^{24} -27y ^ 6[/tex]

So:

We rewrite [tex]8x^{24}\ as\ (2x ^ 8) ^ 3[/tex]

We rewrite[tex]27y ^ 6\ as\ (3y ^ 2) ^ 3[/tex]

(2x ^ 8) ^ 3- (3y ^ 2) ^ 3

Since both terms are perfect cubes, factor using the cube difference formula:

[tex]a ^ 3-b ^ 3 = (a-b) (a ^ 2 + ab + b ^ 2)[/tex]

Where:

[tex]a = 2x ^ 8\\b = 3y ^ 2[/tex]

Rewriting:

[tex](2x ^ 8-3y ^ 2) ((2x ^ 8) ^ 2 + (2x ^ 8) (3y ^ 2) + (3y ^ 2) ^ 2) =\\(2x ^ 8-3y ^ 2) (4x ^{16} + 6x ^ 8y ^ 2 + 9y ^ 4)[/tex]

ANswer:

Option C

Answer:

The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is -80 feet per second.

Step-by-step explanation:

The function that models the height of the ball is:

[tex]f(t)=-16t^2+48t=160[/tex]

At t=3, [tex]f(3)=-16(3)^2+48(3)+160=160[/tex]

At t=5, [tex]f(5)=-16(5)^2+48(5)+160=0[/tex]

The average rate of change is simply the slope of the secant line connecting.

[tex](3,f(3))[/tex] and [tex](5,f(5))[/tex].

The average rate of change

[tex]=\frac{f(3)-f(5)}{3-5}[/tex]

[tex]=\frac{160-0}{-2}[/tex]

[tex]=-80fts^{-1}[/tex]

It will take them 30 minutes

The faster computer will take approximately 22.5 minutes to do the job on its own.

Let's assume that the faster computer can complete the job on its own in x minutes.

If the slower computer takes 45 minutes to complete the job on its own, it means that in 1 minute it completes 1/45th of the job.

Working together, the two computers can complete the entire job in 15 minutes. So in 1 minute, they can complete 1/15th of the job.

Therefore, 1/45 + 1/x = 1/15

Simplifying the equation, we get 1/x = 1/15 - 1/45

Substituting the numerator values with a common denominator, 1/x = (3/45) - (1/45) = 2/45

Now, solving for x, we get x = 45/2 = 22.5

So, it will take the faster computer approximately 22.5 minutes to do the job on its own.

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Answer:

[tex]3a^4[/tex]

Step-by-step explanation:

Given expression is [tex]27a^{12}[/tex].

Now we need to find the cube root of given expression [tex]27a^{12}[/tex].

[tex]\sqrt[3]{27a^{12}}[/tex]

[tex]=\sqrt[3]{3*3*3a^{4*3}}[/tex]

[tex]=\sqrt[3]{3^3\left(a^4\right)^3}[/tex]

[tex]=\sqrt[3]{\left(3a^4\right)^3}[/tex]

Since cube root and cube are opposite operations of each other. So they will cancel each other.

[tex]=3a^4[/tex]

Hence correct choice is the last choice [tex]3a^4[/tex].

Answer:

430/5*9 = 774 miles

Step-by-step explanation: