Mathematics College

30 mm
40 mm
What is the length of the hypotenuse?

Answers

Answer 1

Answer:

50 mm

Step-by-step explanation:

I remembered the 345 triangle, so it applies here.

Related Questions

If Vernie eats 12 cookies which represents 25%of the bag then how many cookies are in the bag

Answers

Answer:

48 cookies

Step-by-step explanation:

Answer:

48 or 36

Step-by-step explanation:

25% of something is also 1/4 of something. This means you would want to multiply 12 by 4 t get 48 total cookies.

I don't know if they are or aren't counting the cookies Vernie ate, if they are counting the ones he ate it would be 48, but if they aren't it would be 48-12=36 since he did eat 12 cookies and they aren't in the bag anymore.

Hope this helps!

Consider rolling dice and getting a total of 8. Find the probability if two dice are rolled. (Enter the value of probability in decimals. Round the answer to three decimal places.)

Answers

Answer:

13.89%

Step-by-step explanation:

The probability when two dices are rolled and their sum is 8 is shown below:

But before that we need to see the probabilities of the sum i.e 8

2 + 6 = 8

3 + 5 = 8

4 + 4 = 8

5 + 3 = 8

6 + 2 = 8

There are 5 outcomes

And, the two dice is 36 i.e square of 6

So, the probability of two dices are rolled and their sum is 8 is

= \(\frac{5}{36}\)

= 13.89%

Fitch & Leeds cans are wrapped in 6 x 200 ml packs. Each pack has the dimensions of 105 mm(W) x 155 mm(L) x 110 mm(H). Calculate the maximum number of packs that can fit into a light delivery vehicle (LDV) if the length of packs of cans are packed against the length of the LDV. top part of the truck 3,02 m the side of the truck 1,88 m top side of the truck 1,08 m

Answers

The number of packs that can fit into the light delivery truck is 3425 packs

How to find the maximum number of packs that can fit into a light delivery vehicle (LDV)

Since Fitch & Leeds cans are wrapped in 6 x 200 ml packs.

Each pack has the dimensions of 105 mm(W) x 155 mm(L) x 110 mm(H), we need to find the volume of each pack. Since each pack is a cuboid, its volume is V = lbh where

l = length = 155 mm w = width = 105 mm h = height = 110 mm

So, the volume of each pack V = lwh

= 155 mm × 105 mm × 110 mm

= 1790250 mm³

Since the length of packs of cans are packed against the length of the LDV. top part of the truck 3,02 m the side of the truck 1,88 m top side of the truck 1,08 m, the truck is also a cuboid. It's volume is V' = LWH

where

l = length = 3.02 m = 3020 mmw = width = 1.88 m = 1880 mm h = height = 1.08 m = 1080 mm

So, the volume of the truck is V' = LWH

= 3020 mm × 1880 mm × 1080 mm

= 6131808000 mm³

So, the number of packs that can fit into the light delivery truck is n = V'/V = 6131808000 mm³/1790250 mm³

= 3425.11

≅ 3425 packs

So, the number of packs that can fit into the light delivery truck is 3425 packs

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You need a 55% alcohol solution. On hand, you have a 550 mL of a 95% alcohol mixture. How much pure water will you need to add to obtain the desired solution?

Answers

Answer:

We need to add 400 ml of pure water to obtain the solution at 55%

Step-by-step explanation:

Concentration

The concentration of a solution measures the amount of solute that has been dissolved in a given amount of solution. The question states the alcohol is the solute and water is the solvent to produce the mix or solution.

The concentration can be calculated with the formula:

\(\displaystyle c=\frac{solute}{solute+solvent}*100\%\)

Originally, the mixture was 95% concentrated.

Substituting in the formula:

\(\displaystyle 95\%=\frac{solute}{solute+solvent}*100\%\)

We know there were 550 ml of solution (solute+solvent), thus

\(solution*0.95=solute=522.5\ ml\)

Now we know there were 522.5 ml of alcohol.

We now need to add x ml of water to have a 55% concentrated solution. Recall that water is solvent, the solute keeps its original value, thus:

\(\displaystyle 55\%=\frac{solute}{550+x}*100\%\)

Operating:

\(0.55(550+x)=522.5\)

Dividing by 0.55

\(550+x=950\)

Thus \(x=950-550=400\)

We need to add 400 ml of pure water to obtain the solution at 55%

Water is pumped out of the conical tank with vertex down and radius 8 ft and height 20 ft. If the volume is decreasing at a rate of 4 ft^3sec :

how fast is the depth of the water decreasing when the water is 9 ft deep? (Note: Don't approximate the answer and state its exact value in terms of π.)

Answers

It took approximately 151 seconds to decrease 9 ft water in conical tank.

The volume of a conical tank with vertex down and radius 8 ft and height 20 ft is V = (1/3)πr²h

When the water is 9 ft deep

= (1/3) ×3.14×(8)²×(9)

= 602.88 ft³

We know that the rate of change of volume is 4 ft³/sec. So, the rate of change of depth can be calculated as follows:

Rate of change of depth (dh/dt) = Volume of tank/4 ft³ per sec

= 602.88/4

= 150.72 sec

Therefore, it took approximately 151 seconds to decrease 9 ft water in conical tank.

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Which mapping diagram does NOT represent a function from x → y?

Answers

Answer:

The correct answer is D

Step-by-step explanation:

the x coordinates on all the other answers don't themselves

hope is helps

have a great day

Evaluate each geometric
series described
3 + 6 +12 + 24 n=7

Answers

Process:

1. 21+24n= 7
2. 24n= 7 - 21
3. 24n= -14

Answ: n= -7/12

Give the domain and range. On a coordinate plane, points are at (negative 2, negative 1), (0, 1), (2, 3). a. domain: {2, 0, 2}, range: {1, 1, 3} b. domain: {–1, 1, 3}, range: {–2, 0, 2} c. domain: {–2, 0, 2}, range: {–1, 1, 3} d. domain: {1, 1, 3}, range: {2, 0, 2} Please select the best answer from the choices provided A B C D

Answers

The correct answer is domain: {-2, 0, 2}, range: {-1, 1, 3}.

Answer:

c. domain: {-2, 0, 2}, range: {-1, 1, 3}

Step-by-step explanation:

From the given points (negative 2, negative 1), (0, 1), (2, 3), we can determine the domain and range.

The domain represents the set of all possible x-values of the points, and the range represents the set of all possible y-values of the points.

In this case, we can see that the x-values are -2, 0, and 2, and the corresponding y-values are -1, 1, and 3.

Therefore, the correct answer is:

c. domain: {-2, 0, 2}, range: {-1, 1, 3}

1. Find the perimeter of the rectangle.

4in w 7in L

O11 in.
O22 in.
O28 in.
O56 in.

Answers

Answer:

(b) 22 in

Step-by-step explanation:

You want the perimeter of a rectangle with side lengths 4 inches and 7 inches.

Perimeter

The perimeter of a rectangle is the sum of the lengths of its sides. Your rectangle has two sides that are 4 inches, and two sides that are 7 inches. The perimeter is the sum of these lengths:

P = 4 in + 4 in + 7 in + 7 in

P = 22 in

The perimeter of the rectangle is 22 inches.

Additional comment

We can save a math operation by recognizing the sum can be arranged to ...

P = (4 in +7 in) +(4 in +7 in) = 2(4 in +7 in)

This is evaluated using one sum and one product, rather than the three sums we need if we simply add the lengths of the four sides.

This is why the usual formula for the perimeter of a rectangle is ...

P = 2(L +W)

This graph shows how fast a commuter train travels on its route in an urban area. What is the meaning of the point with an x-coordinate of 4

Answers

The meaning of the point with an x-coordinate of 2 is in 2 seconds, the commuter travels 120 feet.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Independent variables represent function inputs that do not depend on other values, while dependent variables represent function outputs that depends on other values.

From the graph, the x coordinate 2, have a y coordinate of 120. Hence:

The meaning of the point with an x-coordinate of 2 is in 2 seconds, the commuter travels 120 feet.

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This graph shows how fast a commuter train travels on its route in an urban area. What is the meaning

Bound
Figure 2.
Jenny would like to buy a new air conditioner for his home. As seen in Figure 2 above he has
3 types of brands that he can consider. The cash price for Daewoo is RM1,899, Daikin at a
price of RM1,699 and last choice is Mitsubishi at a price of RM1.999. He plans to make 18
monthly instalments, if he pays RM300 as a down payment for the air conditioner that he would
like to buy, find the interest charge for each brand if the interest rate is 4% based on originall
balance if he chooses to buy from Daikin, find the monthly instalment price and instalment
price that he needs to pay.

Answers

if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

How to determine the monthly instalment price and instalment price that Daikin needs to pay.

Calculating the loan amount for each brand by subtracting the down payment from the cash price:

Loan amount for Daewoo = RM1,899 - RM300 = RM1,599

Loan amount for Daikin = RM1,699 - RM300 = RM1,399

Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699

Calculating the interest charge for each brand:

Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96

Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96

Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96

To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:

Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22

Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89

Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72

Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

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A shoe manufacturer claims that among the general adult population in the United States that the length of the left foot is longer than the length of the right foot. To compare the average length of the left foot with that of the right foot, we will take a random sample of adults and measure the length of the left foot and then the length of the right foot. Based on our sample, does the data indicate that the length of the left foot is greater than the length of the right foot? Is the hypothesis one-tailed or two-tailed?

Answers

We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot.

How to test the data indicate that the length of the left foot is greater than the length of the right foot?

A statistical test is required to determine whether the length of the left foot is greater than the length of the right foot. The null hypothesis states that there is no difference in average length between the left and right feet. The alternative hypothesis is that the left foot's average length is greater than the right foot's average length.

This hypothesis is one-tailed, as we are only interested in whether the left foot is longer than the right foot. We are not considering the possibility that the right foot could be longer than the left foot.

A t-test can be used to determine whether the difference in average length between the left and right feet is statistically significant. We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot if the p-value of the t-test is less than the chosen significance level (e.g., 0.05).

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Eliminate the variable t from the set of parametric equations. Graph the equation X=5cost Y=5sint Please explain this, I need to know how to do these kinds of equations for my trig final

Answers

Answer:

x^2 + y^2 = 25

Step-by-step explanation:

x = 5 cos t

cos t = x/5

y = 5 sin t

sin t = y/5

cos^2 t + sin^2 t = 1

(x/5)^2 + (y/5)^2 = 1

x^2/25 + y^2/25 = 1

(x^2 + y^2)/25 =1

x^2 + y^2 = 25

Which option is an even function?

Answers

The correct answer is option D. Which is the even function is f (x) = x⁴.

What is an even function?

The function in which when the sign of the input variable is changed the output remains the same is called the even function. Mathematically we can write it as f(x) = f(-x ).

let us check the given four options:-

A f(x) = √x ; f(-x) = √-x here f(x) ≠ f(-x)

B f(x) = x ; f(-x) = -x here f(x) ≠ f(-x)

C f(x) = x³ + 1 ; f(-x) = -x³ + 1 here f(x) ≠ f(-x)

D f(x) = x⁴ ; f(-x) = (-x)⁴ = x⁴ here f(x) = f(-x)

We can see that in the option D the f(x) = x⁴ is an even function because f(x) = f(-x).

Therefore the correct answer is option D. Which is the even function is f (x) = x⁴.

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The points plotted below are on the graph of a polynomial. Some of the roots to this polynomial are integers. Which of the following x-values are roots of the polynomial? Check all that apply.

Answers

Answer:

I think its B but I have very little evidence. Don't even put B but I was just saying I think it is.

Step-by-step explanation:

The marked price of a mobile set is Rs3500 and the shopkeeper allows of 10%discount? (I) find the amount of discount. (ii)How much should a customer pay for it after discount.

Answers

Step-by-step explanation:

3500 × 10/100

rs. 350 is the discount

and to find the amnt the customer should pay subtract 350 from 3500

which is,

3150 Rupees

An AP has first term as 3 and Common difference of 2 how many terms are needed to make the sum to 99

Answers

Answer:

Step-by-step explanation:

The \(n\)term is \(2n+1\).

\(S_n=\frac{3+2n+1}{2}(n)=99 \\ \\ \frac{n(2n+4)}{2}=99 \\ \\ n(n+2)=99 \\ \\ n^2+2n-99=0 \\ \\ (n+11)(n-9)=0 \\ \\ n=9 \text{ } (n>0)\)

The number of terms that needed to make the sum to 99 is 9

The first term of the arithmetic progression = 3

The common difference = 2

The sum of n term is = (n/2) [2a+(n-1)d]

Where a is the initial term

d is the common difference

Substitute the values in the equation

(n/2) [2(3)+(n-1)2] = 99

(n/2) [6 + 2n - 2] = 99

(n/2)[4+2n] = 99

n(2 + n) = 99

2n + \(n^2\) = 99

\(n^2\) + 2n - 99 = 0

Split the terms

\(n^2\) - 9n +11n - 99 =0

n(n -9) + 11(n - 9) = 0

(n + 11)(n - 9) = 0

n = -11 or 9

Since n cannot be a negative number, therefore n = 9

Hence, the number of terms that needed to make the sum to 99 is 9

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Use the distributive property to find the equivalent expression.
10(8 + 3h) =

Answers

Answer:

80+30h

Step-by-step explanation:

Use the distributive property to find the equivalent expression.10(8 + 3h) =

if c is (5x-7) degrees and b is (8x-55) degrees what is the value of x

Answers

The value of x is 18 if ∠C and ∠D are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55.

What are vertically opposite angles?

It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.

It is given that:

∠C and ∠D are vertical angles.

From the definition of the vertically opposite angles:

5x-7 = 8x-55

After solving we get:

-7 = 3x -55

3x = 48

x = 16

Thus, the value of x is 18 if ∠C and ∠D are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55.

The complete question is:

∠C and ∠D are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55. What is m∠D ?

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I need help , any of u guys have the answer?

Answers

the answer the third choice
(x to the power of 2+1)+(5-x)
first, u keep x to the power of two because there are no like terms, and then you combine the like terms 1 and 5 to get 6, then you subtract x

therefore, the answer is x squared minus x plus 6

If y varies directly as x and z, and Y =8/3when x = 1 andz = 4, find y when x = 6 andz = 3.
3

Answers

Answer:

y = 12.

Step-by-step explanation:

y = kxz where k is a constant

When x=1,y = 8/3 and z = 4:

8/3 = 1*4k

k = 8/3 * 1/4

k = 2/3.

So our equation of variation is y = 2/3 xz

When x = 6 and z = 3

y = 2/3 * 3 * 6

y = 2 * 6

y = 12.

Answer: its D

Step-by-step explanation:

Part D
Now use GeoGebra to measure the lengths of segments AB and BC and calculate the area of rectangle ABCD. Do you get the same result that you obtained in part C? Take a screenshot with the lengths of the sides labeled and the area displayed, and paste it below.

Answers

Answer:

id ont givea

efijhaoieuvbhzoiubhoewivbawzoufhbealivjhbr

Step-by-step explanation:

idsifui piuh vSeth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Which of these could be a step to prove that BC2 = AB2 + AC2?Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity: