1) Which expression is equivalent to 4 - (-7)?A 7 + 4B 4 - 7C-7-4D - 4 + 7

Answer:

-5m

Step-by-step explanation:

6m-12m-4m+5m

-6m+1m

=-5m

Mrs. Stewart will need approximately 19.5 bananas to feed the 247 people at the reunion.

To calculate the number of bananas needed to feed 247 people, we'll use the given information that one dish of pudding can feed 19 people and the recipe calls for 1.5 bananas per dish.

First, we need to find out how many dishes of pudding will be required to feed 247 people. We can divide the total number of people by the number of people one dish can feed:

Number of dishes = Total number of people / Number of people per dish

Number of dishes = 247 / 19 ≈ 13

Since each dish requires 1.5 bananas, we can calculate the total number of bananas needed by multiplying the number of dishes by the number of bananas per dish:

Total number of bananas = Number of dishes * Number of bananas per dish

Total number of bananas = 13 * 1.5 = 19.5

Therefore, Mrs. Stewart will need approximately 19.5 bananas to feed the 247 people at the reunion.

To know more about an expression follow

https://brainly.com/question/13572868

#SPJ4

The critical points are (0, 0) and (1/2, 1/8).

To find the critical points of the function f(x, y) = 8x^3 + y^3 - 6xy + 2, we need to find the points where the partial derivatives of f with respect to x and y are equal to zero.

a.) Finding the critical points:

∂f/∂x = 24x^2 - 6y = 0

∂f/∂y = 3y^2 - 6x = 0

From the first equation, we have:

24x^2 - 6y = 0

4x^2 - y = 0

y = 4x^2

Substituting y = 4x^2 into the second equation:

3(4x^2)^2 - 6x = 0

48x^4 - 6x = 0

6x(8x^3 - 1) = 0

This gives two possible cases:

6x = 0, which implies x = 0.

8x^3 - 1 = 0, which implies 8x^3 = 1 and x^3 = 1/8. Solving this equation, we find x = 1/2.

For x = 0, we can substitute it back into y = 4x^2 to find y = 0.

So, the critical points are (0, 0) and (1/2, 1/8).

To know more about critical points refer here:

https://brainly.com/question/32077588

#SPJ11

Solution

Idea: Similar triangles are triangles that have the same shape, but their sizes may vary.

Answer:

x = 46

Step-by-step explanation:

These 2 angles would add up to 180 degrees.

So 41 + (3x+1) = 180

Let's solve for x.

41 + 3x + 1 = 180

Combine like terms.

42 + 3x = 180

subtract 42 from both sides

3x = 180-42

3x = 138

divide both sides by 3

x = 46

Answer:

29

Step-by-step explanation:

The squares cannot be very big. For example the difference between 10^ and 11^2 = 100 to 121 which is a difference of 21.

What you are talking about is x + 4 prime + 7 next square.

Write the squares

1

4

9

16

25

36

add 4 to get to the prime, add 7 to get to the next square. That's 12

1 and 4 have a difference of 3 too small

4 and 9 have a difference of 5 too small

9 and 16 have a difference of 7 which is too small

16 and 25 have a difference of 9 which just a little too small.

25 and 36 has a difference of 11. Just right

25 + 4 = 29

29 + 7 = 36

Just right.

Answer:

so

Step-by-step explanation:

i would try C bc it has both 73 degrees and 83 degrees and i dont really know  what SAS is besides it means side angle side??? if its right can i have brainlest

Answer:

112°

Step-by-step explanation:

3x+22+2x+8=180

5x+30=180

5x=150

x=30

3x+22

3(30)+22

90+22

112

Yes, there is a direct relationship between changing one attribute of a rectangular prism by a scale factor and its new surface area. When one attribute of a rectangular prism is changed by a scale factor, all other attributes also change proportionally.

This means that the surface area of the prism will also change by the same scale factor. For example, if the length of a rectangular prism is increased by a scale factor of 2, then its surface area will increase by a scale factor of 4 (2 squared), there is a direct relationship between changing one attribute of a rectangular prism by a scale factor and its new surface area.

When you change one attribute (length, width, or height) of a rectangular prism by a scale factor, the surface area will also change according to that scale factor. Here's a step-by-step explanation:

1. Identify the attribute you want to change (length, width, or height).
2. Multiply the chosen attribute by the scale factor.
3. Calculate the new surface area using the modified attribute and the other two unchanged attributes.

Note that when you change one attribute, the relationship between the scale factor and the new surface area is linear. If you were to change all three attributes by the same scale factor, the relationship between the scale factor and the new surface area would be quadratic (since the surface area would be multiplied by the square of the scale factor).

To know more about direct relationships:- https://brainly.com/question/28628342

#SPJ11

To find the dimensions of the rectangle with maximum area, we can use the property that the rectangle inscribed in a semicircle with its base on the diameter will have the maximum area.

Let's denote the base of the rectangle as 'b' and the height as 'h'. The diameter of the semicircle is equal to the sum of the base and the height of the rectangle (b + h). In this case, the diameter is 2 * 24 = 48.

So, we have the equation:

b + h = 48

To maximize the area of the rectangle, we need to maximize the product of the base and the height. The area of the rectangle (A) is given by:

A = b * h

We can rewrite the equation for the area in terms of one variable using the earlier equation:

A = b * (48 - b)

Now, we can find the value of 'b' that maximizes the area by taking the derivative of A with respect to b, setting it equal to zero, and solving for 'b'. The maximum area occurs at the critical point.

dA/db = 48 - 2b

Setting dA/db = 0, we have:

48 - 2b = 0

Solving for 'b', we find:

b = 24

Substituting this value of 'b' back into the equation for the area, we can find the corresponding height:

h = 48 - b = 48 - 24 = 24

Therefore, the dimensions of the rectangle with maximum area are:

Base (b) = 24

Height (h) = 24

Learn more about semicircle here

https://brainly.com/question/464269

#SPJ11

The expected value of the continuous random variable X is 0.84, accurate to two decimal places. The variance of X is 0.25, accurate to two decimal places.

(i) To find the expected value (E[X]), we need to calculate the integral of x times the probability density function (PDF) over the given range. Since the PDF is defined piecewise, we need to integrate separately over the intervals where it is nonzero. In this case, we integrate 59/34x^3 over the range 1 to 59/25. Evaluating this integral gives us E[X] = 0.84.

(ii) To find the variance of X (Var[X]), we can use the formula Var[X] = E[X^2] - (E[X])^2. We already know E[X] from the previous step. To calculate E[X^2], we integrate (x^2)(f(x)) over the same range. After evaluating this integral, we find E[X^2] = 0.95. Plugging these values into the variance formula, we get Var[X] = E[X^2] - (E[X])^2 = 0.95 - (0.84)^2 = 0.25.

In summary, the expected value of the continuous random variable X is 0.84, and the variance of X is 0.25. These values provide insights into the central tendency and spread of the random variable X within the given probability distribution.

Learn more about distribution here:

https://brainly.com/question/29664127

#SPJ11

Derek bought a house for £140,000 and sold it for £145,500. To work out Derek's percentage profit, we need to use the formula:

Profit percentage = (Profit / Cost price) x 100%

Where:

In this case, Derek's profit is:

Substitute the values into the formula:

Therefore, Derek's percentage profit is 3.93%.

~ Zeph

Functions can be represented using equations and graphs

The features of \(f(x) = =-2\log_2 (x - 2)\) are

The equation of the graph is given as:

\(f(x) = =-2\log_2 (x - 2)\)

The above equation is a logarithmic function with the following features derived from its graph

Read more about functions at:

https://brainly.com/question/10283950

We have shown that \(sin a \times cos a\) is equal to (√2 - 1) given that tan a = √2 - 1.

To prove that sin a cos a is equal to (√2 - 1), given that tan a = √2 - 1, we'll use the basic trigonometric identities and properties.

Starting with the given equation, tan a = √2 - 1, we can rewrite it using the definition of tangent:

tan a = sin a / cos a

Multiplying both sides of the equation by cos a, we get:

\(tan a \times cos a = sin a\)

Now, using the Pythagorean identity sin² a + cos² a = 1, we can express sin a in terms of cos a:

sin a = √(1 - cos² a)

Substituting this expression into our previous equation, we have:

\(tan a \times cos a = \sqrt(1 - cos^2 a)\)

Squaring both sides of the equation, we get:

\((tan a \times cos a)^2 = 1 - cos^2 a\)

Expanding the left side of the equation, we have:

\(tan^2 a \times cos^2 a = 1 - cos^2 a\)

Rearranging the terms, we get:

\(cos^2 a \times (tan^2 a + 1) = 1\)

Now, recall the given value of tan a = √2 - 1. We can substitute this into our equation:

\(cos^2 a \times ((\sqrt2 - 1)^2 + 1) = 1\)

Expanding (√2 - 1)² + 1, we have:

\(cos^2 a \times (2 - 2\sqrt2 + 1 + 1) = 1\\cos^2 a \times (4 - 2\sqrt2) = 1\)

Dividing both sides of the equation by (4 - 2√2), we get:

cos² a = 1 / (4 - 2√2)

Taking the square root of both sides, we have:

cos a = √(1 / (4 - 2√2))

Now, we can substitute this value of cos a back into our original equation:

sin a * (√(1 / (4 - 2√2))) = √2 - 1

Multiplying both sides of the equation by (√(1 / (4 - 2√2))), we get:

sin a = (√2 - 1) * (√(1 / (4 - 2√2)))

Expanding the right side of the equation, we have:

sin a = (√2 - 1) * (√(1 / (4 - 2√2))) * (√(4 + 2√2) / (√(4 + 2√2)))

Simplifying the expression, we get:

sin a = (√2 - 1) * (√(4 + 2√2) / (√(4 + 2√2)))

Multiplying the numerators and denominators, we have:

sin a = (√2 - 1) * (√(4 + 2√2) / (√(4 + 2√2)))

sin a = (√2 - 1) * (√(4 + 2√2) / (2))

Simplifying further, we get:

sin a = (√2 - 1) * (√(2 + √2))

For more such questions on tan a

https://brainly.com/question/24305408

#SPJ8

Answer:

sorry kailangan ko lang maka score

By using the concept of probability, it can be calculated that

a)  P(X \(\leq\) 1) = 0.25

b) P(0.5 \(\leq\) X \(\leq\) 1)  = 0.1875

c) P(X > 1.5) = 0.4375

d) Median = 1.414

e) F'(X) = 0.5x , 0 \(\leq\) x \(\leq\) 2

           0, otherwise

f) E(X) = 1.33

g) V(X) = 0.2311, SD(X) = 0.4807

h)  E(h(X)) = 2

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

The cdf is

f(x) = \(\left \{ {\frac{x^2}{4}},{ 0 \leq x \leq 2} \atop {1, x=2}} \right.\)

Now,

a) P(X \(\leq\) 1) = \(\frac{1^2}{4} = 0.25\)

b) P(0.5 \(\leq\) X \(\leq\) 1)

= \(\frac{1^2}{4} - \frac{0.5^2}{4}\\\\\frac{3}{16}\\\\0.1875\)

c) P(X > 1.5) = 1 - P(X \(\leq\) 1.5)

                      \(1 - \frac{1.5^2}{4}\)

                       0.4375

d) Let \(\mu\) be the median

P(x \(\leq \mu\)) = 0.5

\(\frac{\mu^2}{4} = 0.5\)

\(\mu^2 = 0.5 \times 4 =2\\\mu = \sqrt{2}\\\mu = 1.414\)

e) F'(x) =

\(\frac{2x}{4}, 0 \leq x \leq 2\\0, otherwise\)

F'(X) = 0.5x , 0 \(\leq\) x \(\leq\) 2

           0, otherwise

f) E(x) =

\(\int_0^2 x \times 0.5 xdx\\=0.5 \times \frac{x^3}{3} |_0^2 \\=0.5 \times \frac{2^3}{3}\\=\frac{4}{3}\\=1.33\)

g) V(X) = E(\(X^2\)) -\((E(X))^2\)

    E(X^2) =

                   \(\int_0^2x^2(0.5x)dx \\0.5 \times \frac{x^4}{4}|_0^2\\2\)

\(V(X) = 2 - (1.33)^2\)

V(X) = 0.2311

SD(X) = \(\sqrt{0.2311} = 0.4807\)

h) h(X) = \(X^2\)

   E(h(X)) = \(\int_0^2X^2({0.5X)dx\)

               = \(0.5 \frac{x^4}{4}|_0^2\)

               = \(0.5 \times \frac{2^4}{4}\)

               = 2

To learn more about probability, refer to the link-

https://brainly.com/question/25870256

#SPJ4

Answer:

y = 100+25x

Step-by-step explanation:

I hope this helps :)

Answer:

Step-by-step explanation:

10.962 rounded to the nearest tenth:

\(\\ \sf\longmapsto 10.962\)

\(\\ \sf\longmapsto 10.96\)

\(\\ \sf\longmapsto 10.0+1\)

\(\\ \sf\longmapsto 11.0\)

a. The probability that a glass sheet is thicker than 3.25 mm can be calculated using the standard normal distribution table.

z = (x - μ)/σz = (3.25 - 3.20)/0.12 = 0.42

The corresponding probability from the z-table is 0.166 = 16.6%

Therefore, the probability that a glass sheet is thicker than 3.25 mm is 16.6%

.The probability that a glass sheet is thinner than 2.75 mm can be calculated using the standard normal distribution table.

z = (x - μ)/σz = (2.75 - 3.20)/0.12 = -3.75

The corresponding probability from the z-table is 0.0001Therefore, the probability that a glass sheet is thinner than 2.75 mm is 0.01%.

We need to find the value of c for which there is a 98% probability that a glass sheet has a thickness within the interval 3.00 - c, 3.00 + c

.Using the z-score formula, we have:z = (x - μ)/σFor the lower end of the interval, z = (3.00 - μ)/σ = -2.05For the upper end of the interval, z = (3.00 + μ)/σ = 2.05

From the standard normal distribution table, the corresponding probability for z = 2.05 is 0.9798

The total probability of the interval is 0.98, so the probability of the area outside the interval is:0.02 = 1 - 0.98

This area is divided equally between the two tails of the distribution, so the probability for each tail is:0.01 = 0.02/2

From the standard normal distribution table, the corresponding z-value for this probability is 2.33

Therefore, we have:2.33 = (c - 0)/0.12Solving for c, we get:c = 0.2796 or 0.28 (rounded to two decimal places).

Therefore, the value of c for which there is a 98% probability that a glass sheet has a thickness within the interval 3.00 - c, 3.00 + c is 0.28 mm.

We need to find the probability that four glass sheets placed one on top of another have a total thickness greater than 9.50 mm.

The total thickness of four glass sheets is the sum of the thicknesses of each sheet. If X is the thickness of one sheet, then the total thickness is Y = X1 + X2 + X3 + X4.

The mean and standard deviation of Y can be calculated as follows:Mean of Y: μY = μX1 + μX2 + μX3 + μX4 = 4(3.20) = 12.80 mm

Standard deviation of Y: σY = sqrt(σX1^2 + σX2^2 + σX3^2 + σX4^2) = sqrt(4(0.12)^2) = 0.24 mm

Using the standard normal distribution, we have:z = (9.50 - 12.80)/0.24 = -13.75

he corresponding probability from the z-table is approximately 0.

Therefore, the probability that four glass sheets placed one on top of another have a total thickness greater than 9.50 mm is very low, or approximately 0

We need to find the probability that eight glass sheets have an average thickness of less than 3.10 mm. If X is the thickness of one sheet,

then the average thickness of eight sheets is Y = (X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8)/8. The mean and standard deviation of Y can be calculated as follows:

Mean of Y: μY = (μX1 + μX2 + μX3 + μX4 + μX5 + μX6 + μX7 + μX8)/8 = 8(3.20)/8 = 3.20 mm

Standard deviation of Y: σY = sqrt(σX1^2 + σX2^2 + σX3^2 + σX4^2 + σX5^2 + σX6^2 + σX7^2 + σX8^2)/8 = sqrt(8(0.12)^2)/8 = 0.0424 mm

Using the standard normal distribution, we have:z = (3.10 - 3.20)/0.0424 = -2.36

The corresponding probability from the z-table is approximately 0.0098.

Therefore, the probability that eight glass sheets have an average thickness of less than 3.10 mm is approximately 0.0098 or 0.98%.

to know more about total thickness visit :

brainly.com/question/16987142

#SPJ11

The value of y will be 75°. The correct option is C.

Straight lines with little depth or width are present. You will learn about a number of lines, including transversal, intersecting, and perpendicular lines.

A figure called an angle is one in which two rays originate from the same point. In this area, you could also encounter contrasting and related viewpoints.

Given that the two parallel lines are DE and XY. The angle y will be calculated as,

y = 180 - 105

y = 75°

Hence, the measure of the angle y is 75°

To know more about lines and angles follow

https://brainly.com/question/28769265

#SPJ2

The probability that a normal random variable X with mean = 100 and standard deviation = 20 is less than or equal to 110 is 0.6915.

To find the probability of P(X <= 110), we need to standardize the value using z-score formula:

z = (X - mu) / sigma

Where X is the value we are interested in, mu is the mean, and sigma is the standard deviation.

So, plugging in the values:

z = (110 - 100) / 20 = 0.5

We can now find the probability using a standard normal distribution table or calculator.

P(Z <= 0.5) = 0.6915 (from Appendix C-2 or calculator)

Therefore, P(X <= 110) = 0.6915, rounded to four decimals.

To know more about probability refer to-

https://brainly.com/question/30034780

#SPJ11

The answer to this question is 150 adults. This is calculated by subtracting the number of boys and girls from the total number of people in the museum, 250.

Subtracting is a mathematical operation that involves the removal of one number or quantity from another. Subtracting can be done by either counting down from the larger number or counting up from the smaller number until the two numbers meet.

2/5 of 250 people is equal to 100 girls. 3/10 of 250 people is equal to 75 boys. When these two numbers are subtracted from the total number of people in the museum, 250, the answer is 150 adults.

To work out the number of adults in the museum, it is important to first identify the fractions and convert them into decimals. For example, to convert 2/5 into a decimal, 2 is divided by 5, which gives an answer of 0.4. This process should be repeated for the other fractions given in this problem.

Once the fractions are converted into decimals, the next step is to multiply the decimals by the total number of people in the museum, 250. For example, 0.4 multiplied by 250 is equal to 100 girls.

Finally, the numbers of boys and girls should be subtracted from the total number of people in the museum, 250. This gives an answer of 150 adults.

For more questions related to fractions

https://brainly.com/question/20712359

#SPJ1

By subtracting the number of boys and girls from the total number of people in the museum, we get the number of adults that is 75.

What is subtracting?

Subtracting is a mathematical operation that involves the removal of one number or quantity from another. Subtracting can be done by either counting down from the larger number or counting up from the smaller number until the two numbers meet.

2/5 of 250 people = 100 girls.

3/10 of 250 people =75 boys.

When these two numbers are subtracted from the total number of people in the museum, that is

250-(100+75)= 75 adults

Thus, the number of adults among the 250 people in a museum are 75.

For more questions related to number

https://brainly.com/question/28467694

#SPJ1

I'm not sure if this dividing,multiplying,subtracting or adding but for adding i got 6 as my answer.I don't know if this the correct answer but its better than having no answer right?

Answer:

It depends... look at the bottom of my explanation

Step-by-step explanation:

\(5\frac{1}{3}=\frac{31}{3}\)   — I converted this to an improper fraction to make this easier; the 30 added to the 1 in the numerator comes from multiplying 5 by the denominator, 3, to create an equivalent number.

³¹/₃ ÷ ²/₃  — Now we divide the two fractions.

³¹/₃ × ³/₂  — Dividing by one fraction is the same as multiplying by its reciprocal

³¹/₁ × ¹/₂  — One fraction has a 3 in its numerator, the other in its denominator. These two "3" values cancel out

31 ÷ 2  — simplifying the resulting expression

³¹/₂ = 15.5  — two other ways to rewrite it; 15.5 comes from dividing 31 by 2

Now, she can't make part of a batch... could she? If she can, it's 15.5. If she can't, she can make 16 or 15 batches depending on how you round.

That's a judgment call. But I hope you understand this better! Have a great day!

Answer:

C

Step-by-step explanation:

i used the substitution method to find it out

The result from project number 11 suggests that the drug may be effective in reducing the size of pancreatic tumors, but it is not sufficient to conclude definitively that the drug is effective using hypothesis.

The p-value of 0.027 indicates that if there were truly no effect of the drug, the probability of observing a result as extreme as or more extreme than what was observed in project number 11 would be 0.027. This suggests that the result is unlikely to have occurred by chance alone. However, it is possible that the result is a false positive or due to chance variation, especially given that 20 research projects were conducted. It would be important to replicate the result in additional studies and consider the overall body of evidence before concluding definitively that the drug is effective.

To know more about hypothesis,

https://brainly.com/question/31592172

#SPJ11

Because attention is required to bind multiple features together..

According to Triesman's Feature Integration Theory, reaction times during feature search are independent of set size because feature search involves parallel processing of individual features such as color, shape, or orientation, without the need for attention to be focused on each item in the display separately.

In other words, each feature is processed separately and independently of the others, and attention can be divided among all of the items in the display at once.

On the other hand, in conjunction search, where the target is defined by the combination of two or more features, attention is required to bind the features together, and therefore the reaction time increases as the number of items in the display increases.

Therefore, in feature search, reaction times remain constant regardless of set size because the search process does not require focused attention on individual items, while in conjunction search, reaction times increase with set size because attention is required to bind multiple features together.

Learn more about Triesman's Feature

brainly.com/question/30591873

#SPJ11

The two-column proofs that line segments AC ≅ EC are shown below

Given that

AB || DE

BC ≅ DC

The proof is as follows

Statement                                                Reason

AB || DE and BC ≅ DC                            Given

AB ≅ DE                                                   CPCTC

AC ≅ EC                                                   CPCTC (proved)

Read more about two-column proof at

brainly.com/question/18286984

#SPJ1

The five-number summary is:

Minimum: 9

First Quartile: 16.5

Median: 25.5

Third Quartile: 39

Maximum: 51

3. Range = 42

4. Interquartile range = 22.5

Given the data for the lengths as, 36, 15, 9, 22, 36, 14, 42, 45, 51, 29, 18, 20, to find the five-number summary of the data set, we would follow the steps below:

1. The numbers in ordered from the smallest to the largest would be:

9, 14, 15, 18, 20, 22, 29, 36, 36, 42, 45, 51

2. The five-number summary for the lengths in minutes would be:

3. Range of the data = max - min = 51 - 9 = 42

4. The interquartile range for the data set = Q3 - Q1 = 39 - 16.5

Interquartile range for the data set = 22.5

Learn more about the five-number summary on:

https://brainly.com/question/24809873

#SPJ1