What is the product of (5t-4)(4t+5)

Answer:

Step-by-step explanation:

no

36 square units make up the larger circle's surface area.

We can use the fact that the smaller circle is tangent to the larger circle and passes through its center to find the area of the larger circle. Since the radius of the smaller circle is tangent to the larger circle, the radius of the larger circle is double the radius of the smaller circle.

Let's call the radius of the smaller circle "r" and the radius of the larger circle "R". We know that R = 2r.

We know that the area of a circle is given by the formula A = πr^2.

We know that the area of the smaller circle is 9 square units, we can use this formula to find the radius:

A = πr^2 => r^2 = 9/π => r = sqrt(9/π)

Now we can use the formula of the area of a circle with R-value to get the area of the larger circle:

A = πR^2 => A = π(2r)^2 => A = 4πr^2 => A = 4π(9/π) => A = 36

So the area of the larger circle is 36 square units

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Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

The measure of the ∠PQS will be 71° , and the measure of the ∠PQR will be 142°.

What is an angle bisector ?

The angle bisector is the line or line segment that divides the angle into two identical portions.

Given that line, QS is bisecting the angle PQR into two angles RQS and PQS.

We know that the angle bisector bisects the two angles into two equal halves , i.e.,

∠ PQS = ∠ RQS

So ; the measure of ∠ PQS will be :

∠ PQS = 71°

So , if we want to calculate the measure of ∠PQR then it can be represented as the sum of two angles.

∠ PQR = ∠PQS + ∠RQS

or

∠PQR = 71° + 71°

or

PQR = 142°

Therefore, the measure of the ∠PQS will be 71° , and the measure of the ∠PQR will be 142°.

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during a six-mile trip, each tire of the giant earthmover makes approximately 878 revolutions.

To calculate the number of revolutions the giant earthmover's tire makes during a six-mile trip, we'll need to find the distance covered by one tire revolution and then divide the total distance by that value.
The diameter of the tire is 11.5 feet. To find the circumference (distance covered in one revolution), use the formula: Circumfrence = π × Diameter, where π (pi) is approximately 3.14. So, the circumference is:
Circumference ≈ 3.14 × 11.5 ≈ 36.11 feet
Next, convert the six-mile trip to feet. Since there are 5,280 feet in a mile, the trip is:
6 miles × 5,280 feet/mile = 31,680 feet
Now, divide the total distance (31,680 feet) by the distance covered in one revolution (36.11 feet):
Revolutions ≈ 31,680 feet ÷ 36.11 feet ≈ 877.57
Round this number to the nearest whole number:
Revolutions ≈ 878

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Answer:

Step-by-step explanation:

Conclusion:

Therefore, 3/10 + 21/100 equals 51/100 as a fraction.

Hoped this helped.

\(BrainiacUser1357\)

0.51000 which as smaller is 0.51

Step-by-step explanation:

simplify 21/ 100 then add 3/10 + 21/100 then simplify 3/10 then you would do 3×10+21/100 which equals 51/100

a. P(Blue) = 4 / (6+4+8) = 4/18 = 2/9

b. P (White or Black) = P(White) + P(Black)= 6/18 + 8/18 = 14/18 = 7/9

c. P(Red) = 0 (No red socks are present in the drawer)

d. P (not white) = P(Blue) + P(Black) = 4/18 + 8/18 = 12/18 = 2/3

e. There are two possible scenarios to get at least 2 socks of the same color. Either we can have 2 socks of the same color or 3 socks of the same color or 4 socks of the same color. The probability of getting at least 2 socks of the same color is the sum of the probabilities of these three cases.

P(getting 2 socks of the same color) = (C(3, 1) × C(6, 2) × C(12, 2)) / C(18, 4) = 0.4809

P(getting 3 socks of the same color) = (C(3, 1) × C(6, 3) × C(8, 1)) / C(18, 4) = 0.0447

P(getting 4 socks of the same color) = (C(3, 1) × C(6, 4)) / C(18, 4) = 0.0015

P(getting at least 2 socks of the same color) = 0.4809 + 0.0447 + 0.0015 = 0.5271So, the required probability is 0.5271.

There are six white socks, four blue socks, and eight black socks in a drawer. One sock is picked out of the drawer, and there is an equal chance that any sock will be selected. The following events' likelihood must be determined:

a) The probability that the sock is blue is found by dividing the number of blue socks by the total number of socks in the drawer.

b) The probability that the sock is white or black is obtained by adding the probability of drawing a white sock and the  probability of drawing a black sock.

c) Since no red socks are present in the drawer, the probability of drawing a red sock is 0.

d) The probability of not choosing a white sock is obtained by adding the probability of selecting a blue sock and the    probability of selecting a black sock.

e) To have at least two socks of the same color, we may either have two, three, or four socks of the same color. We  find the probabilities of each case and add them up to get the probability of at least two socks of the same color.

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Answer:

all of them are much larger except number 2 which is close to 1

Step-by-step explanation:

The difference in the dollar value of Assistantship (Stipend) between art and science fields with  standard errors is equal to 1.214.

Mean      24041.62203                 25952.36501

Sample mean difference between Assistantship (stipend) in arts and science is equal to

=  $25952.36501 - $24041.62203

= $1910.74298.

Hypothesized mean difference is 0 (there is no difference in stipend between the two fields).

Variance        621483.0801            615193.5853

Sample size    521                             479

Standard error of the difference is,

=√[(variance in arts / sample size in arts) + (variance in science / sample size in science)]

= √[(615193.5853 / 479) + (621483.0801 / 521)]

= $49.77

t-statistic

= (sample mean difference - hypothesized mean difference) / standard error of the difference

Substitute the values into the t-statistic formula,

⇒ t-statistic = ($1910.74298 - 0) / $49.77

⇒ t-statistic = 38.39

t-critical value for a two-tailed test with 992 degrees of freedom at a significance level of 0.05 is 1.9624.

t-statistic (38.39) > t-critical value (1.9624)

⇒Reject the null hypothesis that there is no difference in stipend between the two fields.

standard errors

= t-statistic / √(sample size)

= 38.39 / √(479 + 521)

= 38.39 /31.62

=1.214

Therefore,  the difference in the dollar value of Assistantship (Stipend) between these two fields is 1.214 standard errors away from the hypothesized difference.

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The total product average product and marginal product are important to operate efficiently and maximize profits. Option D is the correct answer.

Being able to calculate the total product, average product, and marginal product is important for businesses to operate efficiently and maximize profits.

The total product is the overall output produced by a business, while the average product is the output per unit of input, and the marginal product is the change in output resulting from a change in input.

These calculations can help businesses optimize their production processes by identifying the most efficient levels of input and output.

By maximizing their output while minimizing their input costs, businesses can increase their profitability and gain a competitive advantage in the market.

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The question is -

Being able to calculate the total product average product and the marginal product is important:

a. for determining demand and supply.

b. when filing taxes.

c. to keep competition in check.

d. to operate efficiently and maximize profits.

Answer:

£42.04 is the correct answer.

Step-by-step explanation:

Cost of pack of 15 bread rolls = £1.91

Cost of pack of 20 cheese slices = £2.23

She has to buy exactly twice as many cheese slices as bread rolls.

She has to make more than 100 cheese sandwiches.

Number of bread rolls required for 100 bread rolls.

Minimum 15\(\times\)7 = 105 bread rolls are to be bought.

105 bread rolls mean 210 cheese slices but it is a pack of 20 cheese slices.

So, at least 220 cheese slices can be bought.

But, 220/2 = 110 bread rolls are not possible to be bought.

So, at least 120 (15 \(\times\) 8 i.e. 8 packs) bread rolls have to be bought and 120 \(\times\) 2 = 240 (20 \(\times\) 12 i.e. 12 packs) of sandwiches have to be bought.

So, minimum amount to be spent for at least 100 cheese sandwiches

= 1.91 \(\times\) 8 + 2.23 \(\times\) 12 = £42.04

Answer:

£42.04

Step-by-step explanation:

Answer:

x^3 + 3x^2 + 3

Step-by-step explanation:

Since this is only addition and subtraction we can remove the parentheses and just do the math.

Answer:

x^3 + 3x^2 + 3

Step-by-step explanation:

parentheses method

The external angle of the triangle is equals to the sum of the 2 opposite angles. Therefore,

Answer:

Vv Vc Vs Vp

Sv Sc Ss Sp

Cv Cc Cs Cp

answer is C = 12

Answer:

\( \hat y = 8.5*2 -5 = 12\)

And the residual is defined as:

\( e_ i = y_i -\hat y_i \)

And replacing we got:

\( e_i = 20-12 = 8\)

Step-by-step explanation:

For this case we know that the amount of money 'y' made at a laundromat after 'x' months can be represented by the linear function:

\( y = 8.50 x -5\)

And fter two months we know that the laundromat made 20 dollars. And if we use the linear function we got:

\( \hat y = 8.5*2 -5 = 12\)

And the residual is defined as:

\( e_ i = y_i -\hat y_i \)

And replacing we got:

\( e_i = 20-12 = 8\)

Consider the same figure as given above. It is observed that DP/PE = DQ/QF and also in the triangle DEF, the line PQ is parallel to the line EF.

So, ∠P = ∠E and ∠Q = ∠F.

Hence, we can write: DP/DE = DQ/DF= PQ/EF.

The above expression is written as

DP/DE = DQ/DF=BC/EF.

It means that PQ = BC.

Hence, the triangle ABC is congruent to the triangle DPQ.

(i.e) ∆ ABC ≅ ∆ DPQ.

Thus, by using the AAA criterion for similarity of the triangle, we can say that

∠A = ∠D, ∠B = ∠E and ∠C = ∠F.

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9514 1404 393

Answer:

  162 degrees

Step-by-step explanation:

Angles P and F are supplementary, so ...

  3x^2 +12x = 180

  x^2 +4x = 60

  x^2 +4x -60 = 0

  (x +10)(x -6) = 0

The useful value of x that makes this true is x=6.

The measure of angle Q is 3x, so is 3·6 = 18 degrees. The measure of angle S is the supplement to that:

  ∠S = 180° -18° = 162°

To predict a linear regression score, you first need to train a linear regression model using a set of training data.

Once the model is trained, you can use it to make predictions on new data points. The predicted score will be based on the linear relationship between the input variables and the target variable,

A higher regression score indicates a better fit, while a lower score indicates a poorer fit.

To predict a linear regression score, follow these steps:

1. Gather your data: Collect the data p

points (x, y) for the variable you want to predict (y) based on the input variable (x).

2. Calculate the means: Find the mean of the x values (x) and the mean of the y values (y).

3. Calculate the slope (b1): Use the formula b1 = Σ[(xi - x)(yi - y)]  Σ(xi - x)^2, where xi and yi are the individual data points, and x and y are the means of x and y, respectively.

4. Calculate the intercept (b0): Use the formula b0 = y - b1 * x, where y is the mean of the y values and x is the mean of the x values.

5. Form the linear equation: The linear equation will be in the form y = b0 + b1 * x, where y is the predicted value, x is the input variable, and b0 and b1 are the intercept and slope, respectively.

6. Predict the linear regression score: Use the linear equation to predict the value of y for any given value of x by plugging in the x value into the equation. The resulting y value is your predicted linear regression score.

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Answer:

z=12

Step-by-step explanation:

Tell me what number can you multiply q (unknown value) and 4 to get 9 and 12.... 3 right? 3x3 is?? 9 exactly. 3x4 is??? 12 boom

The probability will be 0.037 or 3.7% when it is rounded to the nearest tenth.

To calculate the probability of hitting the clown's mouth, we need to compare the area of the clown's mouth to the total area of the rectangular wood piece.

The area of the clown's mouth can be found using the formula for the area of a circle: A = π * (r^2), where r is the radius. In this case, the diameter is given as 3 inches, so the radius is 1.5 inches.

Plugging the values into the formula, we get A = π * (1.5^2) = 7.065 square inches. The total area of the rectangular wood piece is 16 inches * 12 inches = 192 square inches.

Therefore, the probability of hitting the clown's mouth is 7.065 / 192 ≈ 0.0367, which rounds to 0.037 or 3.7% when expressed as a percentage rounded to the nearest tenth.

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The ratio commonly used as an alternative to 3.14 in mathematical calculations is 22/7, which is equivalent to 3.142857142857143.

This ratio 22/7 is often used as an approximation for pi (π), which is a mathematical constant representing the ratio of a circle's circumference to its diameter.

Although 22/7 is not an exact representation of pi, it is a simple and convenient alternative that is easy to remember and use in calculations. In fact, 22/7 is often accurate enough for most practical purposes, such as calculating the area or volume of simple geometric shapes.

However, for more complex calculations or applications that require a high degree of accuracy, it is necessary to use the actual value of pi, which is an irrational number that cannot be expressed as a simple fraction.

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Answer:

a loss of 72.47

Step-by-step explanation:

I got this answer right on my test

In the problem given:

W + 15x - 9y + 2z

The term are single mathematical expressions that separate values.

In the expression, there is a + and -; these concludes 2 terms.

There are 3 coefficients next to each variable.

The coefficients are 15x, -9y, and 2z.

That means there are 3 coefficients.

Cheers

- ROR

\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

____________________________________

\( \large \tt Solution \: : \)

Term refers to each variable or constant separated by a mathematical operator.

Coefficient refers to the numberic part of variable or a constant number present in an expression.

\(\qquad \tt \rightarrow \: 12a - 10b + 6\)

\( \large\textsf{Terms :} \)

\( \texttt{coefficient = 1} \)

\( \texttt{coefficient = 15} \)

\( \texttt{coefficient = -9} \)

\( \texttt{coefficient= 2} \)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

5 x 6 = 30

9 x 6 = 54

54 + 30 = 84

you would be intaking 84 grams of fat

Answer:

34.5 feets

Step-by-step explanation:

Length of ladder = 37 feet

Angle between ladder and top of building = 21°

Since ladder makes a right angle with the foot of the wall;

Angle the ladder makes with the ground :

(90° + 21° + θ) = 180°

111° + θ = 180°

θ = 180° - 111°

θ = 69°

To obtain the height, x of the building reached by the ladder ;

Using Pythagoras :

Sinθ = opposite / hypotenus

Sin 69° = x / 37

x = 37 * sin 69°

x = 37 * 0.9335804

x = 34.542475

x = 34.54 feets

Hence, the height up the building reached by the ladder is 34.5 feets

Answer:

the selling price is 21 dollars

The system of linear equation that represent this problem is

6x + 10y = 900

10x + 4y = 1220

Let's represent the number of CDs Roberto bought as x and the number of magazines as y

The problem states the following information:

Using the variables;  x and y as given;

1. Roberto bought 6 CDs and 10 magazines for $900.00 pesos. This can be represented as the equation:

  6x + 10y = 900

2. María bought 10 CDs and 4 magazines for $1,220.00 pesos. This can be represented as the equation:

  10x + 4y = 1220

So, the system of equations representing the problem is:

6x + 10y = 900

10x + 4y = 1220

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Translation: Roberto bought 6 cd's and 10 magazines for $900.00 pesos; In the same store, her friend María bought 10 CDs and 4

magazines at $1,220.00 pesos. What is the system of equations with two unknowns that represents the problem?

The function whose vertex is on the y-axis is f(x) = (x – 2)(x + 2).

Option C is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Write each of the functions in the form of ax² + bx + c

Vertex of the function.

= ( -b/2a, f(-b/2a) )

Now,

f(x) = (x – 2)²

x² - 2x + 4

a = 1, b = -2, c = 4

-b/2a = 2/2 = 1

f(1) = -2

Vertex = (1, -2)

f(x) = x(x + 2)

x² + 2x

a = 1, b = 2, c = 0

-b/2a = -2/2 = -1

f(-1) = -1(-1 + 2) = -1

Vertext = (-1, -1)

f(x) = (x – 2)(x + 2)

x² + 2x - 2x + 4

x² + 4

a = 1, b = 0, c = 4

-b/2a = 0

f(0) = (0 -2)(0 + 2) = -4

Vertex = (0, -4)

f(x) = (x + 1)(x – 2)

x² - 2x + x - 2

x² -  x + 2

a = 1, b = -1, c = 2

-b/2a = 1/2

f(1/2) = (1/2 + 1)(1/2 - 2) = 3/2 x -3/2 = -9/4

Vertex = (1/2, -9/4)

Thus,

The vertex (0, -4) is on the y-axis.

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