The number of apples in a fruit basket is
directly proportional to the number of
oranges. If there are 2 apples and 5 oranges
in Mary's basket, how many more apples are
there in a basket that contains 35 oranges?

a) The statement "If hog is injective, then gg is injective" is true. b) The statement "If hog is injective, then h is injective" is false.c) The statement "If hog is surjective and h is injective, then g is surjective" is true.

a) The statement "If hog is injective, then gg is injective" is true.

Proof: Let's assume that hog is injective. To prove that gg is injective, we need to show that for any elements x₁ and x₂ in X, if gg(x₁) = gg(x₂), then x₁ = x₂.

Since gg(x) = g(g(x)) for any x in X, we can rewrite the assumption as follows: for any x₁ and x₂ in X, if g(h(x₁)) = g(h(x₂)), then x₁ = x₂.

Now, if g(h(x₁)) = g(h(x₂)), by the injectivity of g (since hog is injective), we can conclude that h(x₁) = h(x₂).

Finally, since h is a function from Y to Z, and h is injective, we can further deduce that x₁ = x₂.

Therefore, we have proved that if hog is injective, then gg is injective.

b) The statement "If hog is injective, then h is injective" is false.

Counterexample: Let's consider the following scenario: X = {1}, Y = {2, 3}, Z = {4}, g(1) = 2, h(2) = 4, h(3) = 4.

In this case, hog is injective since there is only one element in X. However, h is not injective since both elements 2 and 3 in Y map to the same element 4 in Z.

Therefore, the statement is false.

c) The statement "If hog is surjective and h is injective, then g is surjective" is true.

Proof: Let's assume that hog is surjective and h is injective. We need to prove that for any element y in Y, there exists an element x in X such that g(x) = y.

Since hog is surjective, for any y in Y, there exists an element x' in X such that hog(x') = y.

Now, let's consider an arbitrary element y in Y. Since h is injective, there is only one pre-image for y, denoted as x' in X.

Therefore, we have g(x') = y, which implies that g is surjective.

Hence, we have proved that if hog is surjective and h is injective, then g is surjective.

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The mean, median, and mode of a distribution are measures of central tendency.

A measure of central tendency of a data set determines its central value. Measures of central tendency are mean median and mode.

Mean is the average of a set of numbers.

Mode refers to a value that appears most frequently in a data set.

Median is the number in the centre of a data set.

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Answer:

A

Step-by-step explanation:

P(X ≥ 200) = 1 - P(X < 200) ≈ 1.0. In other words, it is very likely (almost certain) that at least 200 out of 210 college graduates under age 20 are employed.

To find the probability that at least 200 out of 210 college graduates under age 20 are employed, we can use the binomial distribution formula:
P(X ≥ 200) = 1 - P(X < 200)
where X is the number of employed college graduates under age 20 out of a sample of 210.
We know that the unemployment rate for college graduates under the age of 20 is 7%. Therefore, the probability of an individual college graduate being unemployed is 0.07.
To find the probability of X employed college graduates out of 210, we can use the binomial distribution formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where n is the sample size (210), k is the number of employed college graduates, and p is the probability of an individual college graduate being employed (1-0.07=0.93).
We want to find P(X < 200), which is the same as finding P(X ≤ 199). We can use the cumulative binomial distribution function on a calculator or software to find this probability:
P(X ≤ 199) = 0.000000000000000000000000000001004 (very small)
Therefore, P(X ≥ 200) = 1 - P(X < 200) ≈ 1.0. In other words, it is very likely (almost certain) that at least 200 out of 210 college graduates under age 20 are employed.

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If the provided SHA hash value is different from the one I calculated, it indicates that there has been a modification or alteration in the data or the process used to calculate the hash.

This inconsistency raises concerns about data integrity and the authenticity of the information.

SHA (Secure Hash Algorithm) is a cryptographic hash function that generates a unique hash value for a given input. It is designed to be highly sensitive to any changes in the input data, meaning even a small alteration in the data will result in a completely different hash value. Therefore, if the provided SHA hash value differs from the one I calculated, it suggests that either the input data has been tampered with, or there is an error in the hash calculation process.

In such a situation, it is important to investigate the cause of the discrepancy and determine the source of the error. It could be due to accidental data corruption, intentional tampering, or an error in the hash calculation algorithm or implementation. Validating the integrity of the data becomes crucial to ensure the accuracy and trustworthiness of the information.

To resolve the issue, a comparison of the original and modified data should be conducted, and the hash calculation process should be carefully reviewed. It is also advisable to verify the integrity of the data through other means, such as using digital signatures or checksums, to detect any unauthorized modifications.

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Answer:

D) \(x=-3,\,x=5\)

Step-by-step explanation:

\(y=x^2-2x-15\\0=x^2-2x-15\\0=x^2-5x+3x-15\\0=x(x-5)+3(x-5)\\0=(x+3)(x-5)\\x=-3,\,x=5\)

Answer:

90°

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

2x – y = (3/4)x + 6

2x - (3/4)x = y + 6

(8x -3x)/4 = y + 6

5x/4 = y + 6

5x = 4(y + 6)

5x = 4y + 24

x = (4y + 24)/5

x = 4(y + 6)/5

The first step is to find the mean number of incorrect answers. Since there are 11 questions, and each question has a 50/50 chance of being answered incorrectly, we can expect the student to get 5.5 questions wrong on average.

Next, we need to calculate the variance. To do this, we can use the formula:

Variance = p(1-p)n

Where p is the probability of getting a question wrong (0.5), and n is the number of questions (11).

Variance = 0.5(1-0.5)11 = 1.375

Finally, we can find the standard deviation by taking the square root of the variance:

Standard deviation = sqrt(1.375) = 1.17 (rounded to two decimal places)

Therefore, the standard deviation of the number of incorrect answers on the exam is 1.17.

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Answer:

B.(3.0)

Step-by-step explanation:

took the test

To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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Answer:

5A)36 5b)30(mark as brainliest)

Step-by-step explanation:

5a)6+6+6+6+12 = 36

5b)36-8=28

28+2 = 30

Answer:

a: The answer is 36 units squared

b: You would lose four square units

Step-by-step explanation:

a: You can count the pieces showing, but you also have to add the amount you cannot see, which would give you a total of 36 units squared (since it doesn't say what each unit is represented by

b: The bottom pieces that originally were not showing would now be showing, but you would lose the ones above it. These cancel out from each other. There are 4 other sides that are now no longer showing since the others that are still showing still were anyways, so there are 4 units squared missing from the surface area when you remove the top two blocks.

Based on the given function, the average temperature in the town between 3 A.M. (t= 3) and 6 A M. (t = 6), in degrees Fahrenheit is 57.797°. (Option B)

The temperature, in degrees Fahrenheit, in a small-town t hours after midnight (t 0) is modeled by the function g(t)= 65 - 8 sin (πt/12). Hence, the average temperature in the town between 3 A.M. (t= 3) and 6 A M. (t = 6), in degrees Fahrenheit is given by:

1/((6-3)) ∫_3^6▒〖(65-8 sin⁡(πt/12)dt〗

65/3 t+  32/π  cos⁡(πt/12)

(65π-16√2)/π

57.797

Note: The question is incomplete. The complete question probably is: On a certain day, the temperature, in degrees Fahrenheit, in a small-town t hours after midnight (t 0) is modeled by the function g(t)= 65 - 8 sin (πt/12). What is the average temperature in the town between 3 A.M. (t= 3) and 6 A M. (t = 6), in degrees Fahrenheit? A) 57.609° B) 57.797° C) 58.172° D) 59.907°.

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Answer:

m = -6

Step-by-step explanation:

3m= 5(m + 3)-3

Distribute

3m = 5m +15 -3

Combine like terms

3m = 5m +12

Subtract 5m

3m-5m = 5m+12-5m

-2m = 12

Divide by -2

-2m/-2 = 12/-2

m = -6

Answer:

B) 5, 20, 80, 320

Step-by-step explanation:

Complete question

Given the recursive formula shown, what are the first 4 terms of the sequence?

f(1) = 5 if n=1

f(n) = 4f(n-1) if n> 1

A) 5. 25, 100, 400

B) 5, 20, 80, 320

C) 5, 25, 125, 625

D) 5. 14, 60, 236

Get f(2)

f(2) = 4f(2-1)

f(2) = 4f(1)

f(2) = 4(5)

f(2) = 20

Get f(3)

f(3) = 4f(3-1)

f(3) = 4f(2)

f(3) = 4(20)

f(3) = 80

Get f(4)

f(4) = 4f(4-1)

f(4) = 4f(3)

f(4) = 4(80)

f(4) = 320

Hence the first 4 terms of the sequence are 5, 20, 80 and 320

Answer:

B) 5, 20, 80, 320

Step-by-step explanation:

To find A.), we must create a linear equation. Let b be the number of books Sam ordered. We write 5b because each book is 5 dollars. Then we add 4 dollars to the equation to represent the shipping fee. Then we write "equals to 89",  because it says that is the total cost. So we get the equation \(5b+\$4=\bold{\$89}\)

To find B.), we must solve the equation. Isolate the variable, by subtracting 4 from both sides. We then get \(5b=\$85\). Now we divide by 5 to get only the variable and to get rid of the coefficient. We get \(b=17\). So Sam bought 17 books.

Answer:

-5

0

5

Step-by-step explanation:

x is being assigned a value of -5:

x -> -5

x will be assigned x's previous value + 5:

x -> x + 5

x will keep increasing by 5 until x = 6, hence the REPEAT UNTIL (x = 6)

so:

-5 is the starting value and:

x -> -5 + 5

x = 0

x -> 0 + 5

x = 5

x -> 5 + 5

x = 10. thats more than 6, so we stop and x = 5

-5

0

5

Answer:

The jazz band visited 124 cities and the rock band visited 53 cities. The solution is viable.

Step-by-step explanation:

Answer:

The jazz band visited 124 cities and the rock band visited 53 cities. The solution is nonviable.

Step-by-step explanation:

Answer:

x = number of packets of strawberry wafers = 4 packets

y = number of packets of chocolate wafers = 18 packets

Step-by-step explanation:

Devon and his friends bought strawberry wafers for $3 per packet and chocolate wafers for $1 per packet at a carnival. They spent a total of $30 to buy a total of 22 packets of wafers of the two varieties.

Part A: Write a system of equations that can be solved to find the number of packets of strawberry wafers and the number of packets of chocolate wafers that Devon and his friends bought at the carnival. Define the variables used in the equations. (5 points)

Part B: How many packets of chocolate wafers and strawberry wafers did they buy? Explain how you got the answer and why you selected a particular method to get the answer. (5 points)

A.

Let

x = number of packets of strawberry wafers

y = number of packets of chocolate wafers

x + y = 22

3x + y = 30

B. Solve the equation in A using elimination method

x + y = 22 (1)

3x + y = 30 (2)

subtract (1) from (2) to eliminate y

3x - x = 30 - 22

2x = 8

x = 8/2

x = 4

Substitute x = 4 into (1) to solve for y

x + y = 22 (1)

4 + y = 22

y = 22 - 4

y = 18

x = number of packets of strawberry wafers = 4 packets

y = number of packets of chocolate wafers = 18 packets

Answer:

225

Step-by-step explanation:

first the square

9*9 = 81

then the triangle

a is 8

triangles are l*w/2 so 8*4.5/2

8*4.5 = 36/2 = 18

There are 8 of these triangles

18*8 is 144

144+81 = 225

The surface area of the square pyramid is approximately `196` square cm.

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

We can use the Pythagorean theorem to find the slant height of the pyramid:

\($$l = \sqrt{a^2 + \left(\frac{b}{2}\right)^2} \\= \sqrt{8^2 + \left(\frac{9}{2}\right)^2} \\= \sqrt{64+\frac{81}{4}} \\= \frac{\sqrt{433}}{2}$$\)

So, the lateral area of the pyramid is the area of the four triangles with base `b` and height `l`, which is:

\($$A_{lat} = 4\cdot\frac{1}{2}b\cdot l \\= 4\cdot\frac{1}{2}\cdot 9 \cdot \frac{\sqrt{433}}{2} \\= 27\sqrt{433}$$\)

So, The area of the base of the pyramid is a² then

\($$A = A_{lat} + a^2$$\)

=  = 27√433 + 8²

= 27√{433} + 64

= 196.4 cm²

Therefore, the surface area of the square pyramid is approximately `196` square cm.

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Using the probability, Carlos should use 4 blocks labeled with a 1 and 1 block labeled with a 0 to represent kicking 5 field goals in a single game with a 72% probability of making each one.

To represent kicking 5 field goals in a single game with a 72% probability of making each one, Carlos can use a block for each kick, and label the block with a 1 to represent making the kick and a 0 to represent missing the kick. Since there are 5 kicks in total, he would need 5 blocks in total.

To determine how many of each block Carlos should use to represent the situation, we need to calculate the probability of making each kick and use it to determine the number of blocks labeled with a 1 and a 0.

Since the probability of making each kick is 72%, the probability of missing each kick is 28% (100% - 72%). Therefore, to represent 5 kicks with a 72% probability of making each one, Carlos should use:

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Answer:

Step-by-step explanation:

11:30-9:30=2

so Danielle starts 2 hrs late.

let Danielle catches them after x hrs.

x×60=(x+2)×20

divide by 20

3x=x+2

3x-x=2

2x=2

x=1

so Danielle takes 1 hour to catches them.

Answer:

9

Step-by-step explanation:

8x-13=5x+14

you subtract 5x from both sides and get

3x-13=14

then add 13 to both sides  and get

3x=27

then divide 3 from both sides

3/3=x

27/3=9

x=9

Answer:

x = 9

Step-by-step explanation:

8x - 13 = 5x + 14                                                                                                                                Subtract 5x from both sides of the equation                                                                    3x - 13 = 14                                                                                                                          Add 13 to both sides of the equation                                                                            3x = 27                                                                                                                                     Divide by 3 for both sides of hte eqation                                                                        x = 9

Answer:

what is this pls isit a question

The length BC of the right triangle is 18 units.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The length BC of the right triangle can be found as follows:

Therefore, using proportion because triangle ABC is similar to triangle BDC.

x / 36 = 9 / x

cross multiply

x × x = 36 × 9

x² = 324

square root both sides of the equation

x = √324

x = 18 units

Therefore,

BC = 18 units

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Without seeing the scatterplot or the data, it is difficult to determine the exact value of x that has the largest absolute prediction error.

However, in general, the x-value with the largest absolute prediction error is typically the x-value that is farthest away from the regression line.

To calculate the prediction error for a given x-value, you can first calculate the predicted y-value for that x-value using the equation of the regression line. Then, you can subtract the actual y-value for that x-value from the predicted y-value to get the prediction error.

The absolute value of the prediction error represents the magnitude of the difference between the actual and predicted values, regardless of whether the prediction was too high or too low. Therefore, to find the x-value with the largest absolute prediction error, you can calculate the absolute prediction error for each x-value and then identify the x-value with the largest value.

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Step-by-step explanation:

The answer is in the picture above

Answer:

1. 2. 4. all have negative answers

Step-by-step explanation:

2 + 2(-3)(7)= -40

-2(27 ÷ 9)+4= -2

(4 - 10) - ( 8 ÷ ( -2))= -2

Hope this helped!

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{30x + 12}}}}}\)

Step-by-step explanation:

\( \sf{6(2x + 1) + 3(6x + 2)}\)

Distribute 6 through the parentheses

Similarly, distribute 3 through the parentheses

\( \dashrightarrow{ \sf{12x + 6 + 18x + 6}}\)

Collect like terms

\( \dashrightarrow{ \sf{12x + 18x + 6 + 6}}\)

\( \dashrightarrow{ \sf{30x + 6 + 6}}\)

Add the numbers : 6 and 6

\( \dashrightarrow{ \sf{30x + 12}}\)

Hope I helped!

Best regards! :D

we have the system

y + z = 6 ------> equation P

5y + 9z = 1 -----> equation Q

i will solve by elimination

step 1

Multiply the equation P by -5

so

(y + z = 6) *-5

-5y-5z=-30

adds equation Q

-5y-5z=-30

5y + 9z = 1

------------------

5z+9z=-30+1

therefore