△H'I'J' is a translation of △HIJ. Write the translation rule.

Answer:

27^4

2.74*10^2

4.27*10^2

Step-by-step explanation:

in exponential notation the number is expressed like this.

Answer:

There are 7,725 square feet of grass on the trapezoidal field

Step-by-step explanation:

Here in this question, we are interested in calculating the square feet of grass present on the trapezoidal field.

What this question is actually asking us is to calculate the area of the trapezoid-shaped grass field.

To calculate this area, what we need to do

simply is to use the formula for the area of a trapezoid.

Mathematically, the area of a trapezoid can be calculated using the formula;

Area of trapezoid = 1/2 * (a + b) * h

where a and b refers to the length of the parallel lengths of the trapezoid and h refers to the height of the trapezoid.

From the question;

a, b = 81ft and 125 ft

h = 75 ft

Substituting these values, we have :

Area = 1/2 * (81 + 125) * 75

Area = 1/2 * 206 * 75 = 83 * 75 = 7,725 ft^2

A logical implication is considered true if the antecedent (p or q or r) implies the consequent (q or p or r), meaning that if the antecedent is true, then the consequent must also be true.

The six possible logical implications between pairs of propositions p, q, and r are:

A logical implication is considered true if the antecedent (p or q or r) implies the consequent (q or p or r), meaning that if the antecedent is true, then the consequent must also be true. However, the converse of the implication may not be true, meaning that if the consequent is true, the antecedent may not be true.

Whether or not any of p, q, and r are logically equivalent to another depends on the specific logical relationships between them. Logical equivalence occurs when two propositions have the same truth value, meaning that they are both true or both false, regardless of the truth values of the other propositions.

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Answer:

put the number over 100 and then simplify it. for example:

50%

50/100 = 1/2

Answer:

Train A = 70km

Train B = 75km

Train B is going faster than Train A.

Step-by-step explanation:

Train B = \( \frac{d}{t} = \frac{150}{2} = 75km\)

Train A = \( \frac{d}{t} = 70km\)

Answer:

The estimate is,

f(117) = 56

Step-by-step explanation:

We use the linear approximation,

L(x) = f(a) + f'(a)(x-a)

In our case,

x = 117,

a = 115

f(115) = f(a) = 50,

f'(a) = f'(115) = 3

Putting all this into the linear approximation equation, we get,

L(117) = f(115) + (f'(115))(117-115)

L(117) = 50 + 3(2)

L(117) = 56

Or, approximately,

f(117) = 56

Answer:

You have the right answer selected

Step-by-step explanation:

Answer:

You are correct.

Step-by-step explanation:

Distribute 16 to 3b to get 48b. Distribute 16 to 0.25 to get 4. Keep the subtraction and end up with 48b - 4.

Answer:

7

Step-by-step explanation:

The solution set for the number line of inequality can be represented as,

{x | x ≤ 4. 5}

The number line is the way of representation of number and digits in a arranged form to understand the data batter.

The meaning of circle in number line,

The number line going from negative 5 to positive 5 and a solid circle appears between positive 4 and positive 5. The middle point of 4 and 5 is 4.5.

The solid or closed circle means that the value has less than or equal to 4.5. Thus, the solution set for the number line of inequality can be represented as,

{x | x ≤ 4. 5}

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Answer:

the answer to x is 15 degrees

Answer:

x = 15

Step-by-step explanation:

these two labeled angles are supplementary because they are same-side interior angles

we can add them together and set the sum equal to 180 to find 'x'

3x - 15 + 150 = 180

combine -15 and 150 to get 135

3x + 135 = 180

subtract 135 from each side to get:

3x = 45

divide each side by 3 to get:

x = 15

the p-value (0.208) is greater than the significance level (0.01), we fail to reject the null hypothesis

To determine if there is evidence to suggest that the proportion of voters who believe pharmaceutical companies invent diseases to make money is different for Democrats and Republicans, we can perform a hypothesis test. Let p1 be the proportion of Democrats who believe in the conspiracy theory, and p2 be the proportion of Republicans who believe in the conspiracy theory.

Let's set up the hypotheses:

Null hypothesis (H0): p1 - p2 = 0 (There is no difference in the proportions of Democrats and Republicans who believe in the conspiracy theory)

Alternative hypothesis (Ha): p1 - p2 ≠ 0 (There is a difference in the proportions of Democrats and Republicans who believe in the conspiracy theory)

We will use a two-sample proportion test to test these hypotheses. The test statistic for this test is given by:

\(\[ Z = \frac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1}+\frac{1}{n_2})}} \]\)

where:

- \(\( \hat{p}_1 \)\) and \(\( \hat{p}_2 \)\) are the sample proportions of Democrats and Republicans who believe in the conspiracy theory, respectively.

- n₁ and n₂ are the sample sizes of Democrats and Republicans, respectively.

- \(\( \hat{p} \)\) is the overall proportion of belief in the conspiracy theory, calculated as the total number of believers divided by the total sample size.

The p-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample data, assuming the null hypothesis is true.

Given the sample data:

Democrats: n₁ = 788 and \(\( \hat{p}_1 = \frac{137}{788} \)\)

Republicans: n₂ = 866 and \(\( \hat{p}_2 = \frac{105}{866} \)\)

Let's calculate the test statistic and the p-value:

Step 1: Calculate \(\( \hat{p} \)\):

Total number of believers = 137 + 105 = 242

Total sample size = 788 + 866 = 1654

\(\( \hat{p} = \frac{242}{1654} \)\)

Step 2: Calculate the test statistic (Z):

\(\[ Z = \frac{\frac{137}{788} - \frac{105}{866}}{\sqrt{\frac{242}{1654} \cdot \left(1 - \frac{242}{1654}\right) \cdot \left(\frac{1}{788} + \frac{1}{866}\right)}} \]\)

≈ -1.258

Step 3: Calculate the p-value using the standard normal distribution table for a two-tailed test.

To calculate the p-value, we need to find the probability that a standard normal distribution is less than or greater than the absolute value of the test statistic. Since the alternative hypothesis is two-sided (p1 ≠ p2), we will calculate the p-value as twice the probability of the test statistic being greater than the absolute value of the calculated z-value.

Using a standard normal distribution table or a statistical software, we find that the p-value is approximately 0.208.

Conclusion:

Since the p-value (0.208) is greater than the significance level (0.01), we fail to reject the null hypothesis. There is insufficient evidence to suggest that the proportion of voters who believe pharmaceutical companies invent diseases to make money is different for Democrats and Republicans.

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The error in performing the operation and writing the answer in standard form is in the step where -21² is calculated incorrectly as -21². The correct calculation for -21² is 441.

Corrected Solution:

To correct the error and accurately perform the operation, let's go through the steps:

Step 1: Expand the expression using the distributive property:

(3 + 2i)(5 - 1) = 3(5) + 3(-1) + 2i(5) + 2i(-1)

= 15 - 3 + 10i - 2i

Step 2: Combine like terms:

= 12 + 8i

Step 3: Write the answer in standard form:

The standard form of a complex number is a + bi, where a and b are real numbers. In this case, a = 12 and b = 8.

Therefore, the correct answer in standard form is 12 + 8i.

The error occurs in the subsequent steps where -21² and 2¡² are calculated incorrectly. The value of -21² is not -21², but rather -441. The expression 2¡² is likely a typographical error or a misinterpretation.

To correct the error, we replace -21² with the correct value of -441:

= 15 + 7i - 441 + 7i + 15

= -426 + 14i

Hence, the correct answer in standard form is -426 + 14i.

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Answer:

9 x 6=  9 x ( 3+3 )

= 9 x 3 + 9 x 3

= 27 + 27

= 54

Step-by-step explanation:

Answer:

364

Step-by-step explanation:

2✖️7=14

5✖️7=35

because 14 is two digits, you move the one and plus it to 35 which makes 36.

Leave the 4, and it becomes 364.

Answer:

\(\Huge \boxed{364}\)

\(\rule[225]{225}{2}\)

Step-by-step explanation:

52 × 7

52 = 50 + 2

50 × 7 = 350

2 × 7 = 14

Adding 350 and 14,

350 + 14 = 364

\(\rule[225]{225}{2}\)

Answer:

1. Not necessarily congruent to EFD, since 2 given sides tells us nothing about their congruency.

2. Congruent to QPR, due to SAS congruency.

3. Congruent to LJK, due to SAA congruency.

1. Let the four consecutive numbers be x, x+1, x+2, x+3

The sum of four consecutive number is already given to us = 70

Therefore

⇒(x)+(x+1)+(x+2)+(x+3)=70  

We need to combine x as we have four x terms in the equation. The next step is to get all of the x’s on one side of the equation and all the numbers on the other side. The same rule applies – whatever you do to one side of the equation, you must do to the other side as well!

⇒4x+6=70⇒4x=64⇒x=16

So, the four numbers are 16, 17, 18 and 19.

Hence, the greatest number among them is 19.

Quotient rule of differentiation.

d/dx(csc x) = (-1)(sin \(x)^{-2}\) (cos x) = -cot x (sin \(x)^{-1}\) = -csc x cot x

d/dx(csc x) = -csc x cot x.

To show that d/dx(csc x) = -csc x cot x, we will use the quotient rule of differentiation.

Recall that csc x is defined as 1/sin x.

Therefore, we can rewrite the function as:

csc x = (sin \(x)^{-1}\)

Taking the derivative of csc x with respect to x using the quotient rule, we get:

d/dx(csc x) = (-1)(sin x) (cos x)

Now we need to simplify this expression using trigonometric identities. Recall that

cot x = cos x/sin x.

Therefore, we can rewrite the above expression as:

d/dx(csc x) = (-1)(sin \(x)^{-2}\) (cos x) = -cot x (sin \(x)^{-1}\) = -csc x cot x

Therefore, we have shown that d/dx(csc x) = -csc x cot x.

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To show that d/dx(csc x) = -csc x cot x, we need to differentiate csc x with respect to x using the chain rule and trigonometric identities.

Recall that csc x is the reciprocal of sin x, so we can write:

csc x = 1/sin x

Then, using the chain rule, we can differentiate csc x as follows:

d/dx(csc x) = d/dx(1/sin x) = -1/sin^2 x * d/dx(sin x)

Now, we can use the derivative of sin x with respect to x, which is cos x:

d/dx(csc x) = -1/sin^2 x * cos x

Next, we can use the identity cot x = cos x/sin x to simplify the expression:

d/dx(csc x) = -cos x/(sin x)^2 = -csc x * cot x

Therefore, we have shown that d/dx(csc x) = -csc x cot x.

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Answer:

True.

Explanation:

When solving equations with unknowns on both sides, it is generally recommended to first deal with the variable terms before dealing with the constant terms. This involves simplifying the equation by combining like terms and isolating the variable on one side of the equation. Once the variable is isolated, you can then solve for its value.\(\)

500 J, is the required work to pull the bucket of water to the top of the well.

From the given question we have the following information

the weight of the bucket is 3kg.

length of rope (h) = 5m

Weight of rope: 7kg

Total weight (rope + bucket) = 10kg

Required Work Done = force × distance travelled (length of rope ) = mgh, where

M = total weight in kg

g--> acceleration due to gravity

h--> length of rope ( height )

g = 10 m/sec² ( default value )

Put all the values in the above formula.

Required work done = 100× 5 = 500 Joules .

So, the bucket of water will require 500J work done for pulling.

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Answer:

I believe would be 9•3•3=81 I hope that helps

The quadratic expression cannot be factorized, because the discriminant is less than 0

The expression is given as:

x²+12x+180

Calculate the discriminant of the expresison using:

D = B² - 4AC

So, we have:

D = 12² - 4* 1 * 180

Evaluate

D = -576

Because the discriminant is less than 0, then the expression cannot be factorized

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Answer:

a)40

b)36

Step-by-step explanation:

Supplementary are angles that add to 180 degrees, so do find the second angle, take 180-140=40

Similarly, Complementary angles are angles that add to 90 degrees, so 90-54=36

Hope this helps! <3

Answer:

A. Translation, Translation

Step-by-step explanation:

The pre-image was translated 1 unit up then it was translated 4 unit to the right.

Answer:

x=5/3

Step-by-step explanation:

Let's solve your equation step-by-step.

2x+4x=10

Step 1: Simplify both sides of the equation.

2x+4x=10

(2x+4x)=10(Combine Like Terms)

6x=10

6x=10

Step 2: Divide both sides by 6.

6x /6 = 10 /6

x= 5 /3

Answer:

5/3 or 1.6 repeated

Step-by-step explanation:

Hope this helps :-)

Answer:

9

Step-by-step explanation:

because the paragraph is telling you 9 of the 18 customers want mustard on their hot dog so the paragraph is telling you de answer

Answer:

57

Step-by-step explanation:

First, write the experimental probability as a fraction in simplest form.

P(mustard)

=

mustard

total

=

mustard

mustard+other

=

30

30+10

=

30

40

=

3

4

The experimental probability is

3

4

.

We can predict the outcome of the second set of trials by assuming that the ratio will be the same as in the first set of trials. Write a proportion by setting the two ratios equal to each other, then solve.

3

4

=

n

76

3

4

(476)

=

n

76

(476) Multiply both sides by (476)

376

= 4n Simplify

228

= 4n Simplify

57

= n Divide both sides by 4

You would expect 57 of the next 76 customers to want mustard.

The answers to both the subparts using probability are shown:

(A) The probability that every sign is unique is 378/845.

(B) The probability that each sign is unique and that the first number is the biggest one among the others is 189/1690.

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.

The probability is calculated by dividing the total number of outcomes by the total number of potential events.

Odds and probability are two different concepts.

Calculating odds involves dividing the probability of an event by the probability that it won't happen.

(A) Since there are three positions for letters and four places for numbers.

Consequently, the final result will be 10⁴×26³.

Since each letter and number should be distinct, the necessary probability is:

= 10 * 9 * 8 * 7 * 26 * 25 * 24 / 10⁴ * 26³

= 378/845

(B) In this instance, the likelihood that the first number will be the greatest among the four numbers is 1/4 because it should be.

In order to obtain the result, multiply the result in (a) by 1/4 as follows:

= 378/845 * 1/4

= 189/1690

Therefore, the answers to both the subparts using probability are shown:

(A) The probability that every sign is unique is 378/845.

(B) The probability that each sign is unique and that the first number is the biggest one among the others is 189/1690.

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The null hypothesis (H0) is that the average time spent studying is 2 hours or less, while the alternative hypothesis (H1 or Ha) is that the average time spent studying is more than 2 hours.

The null hypothesis (H0) is a statement of no effect or no difference, while the alternative hypothesis (H1 or Ha) is a statement of the opposite, suggesting that there is an effect or a difference.

In this case, the professor does not believe that his students spend 2 hours on average studying for the final exam and thinks they spend more time than that.

The null hypothesis (H0) would be that the average time spent studying for the final exam is indeed 2 hours or less:

H0: μ ≤ 2

The alternative hypothesis (H1 or Ha) would be that the average time spent studying for the final exam is more than 2 hours:

Ha: μ > 2

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Answer:

\(\sf \dfrac{17}{25}\)

Step-by-step explanation:

    \(\sf \boxed{\bf Tan \ B=\dfrac{oppoiste \ side \ to \ Tan \ B}{hypotenuse}}\)

         \(\sf tan \ B =\dfrac{17}{25}\)