find values of m and n please!

Based on the information of an equilateral triangle △STU and the congruence of angles ∠TXU and ∠TVS, it can be concluded that UX is congruent (≅) to SV. The proof involves establishing the congruence of corresponding angles and applying the angle-angle (AA) congruence criterion.

To prove that UX is congruent (≅) to SV using the information, we will utilize the fact that △STU is an equilateral triangle and the congruence of angles ∠TXU and ∠TVS.

We have:

△STU is an equilateral triangle (∠STU = ∠TUS = ∠UST = 60 degrees)

∠TXU ≅ ∠TVS

Proof:

1. Draw a diagram of equilateral triangle △STU.

2. Draw a line segment UX and SV originating from U and S, respectively, towards the interior of the triangle.

3. ∠TXU and ∠TVS are congruent (given).

4. ∠STU = ∠TUS = ∠UST = 60 degrees (equilateral triangle property).

5. Since ∠STU and ∠TUS are both equal to 60 degrees and ∠TXU ≅ ∠TVS, we can conclude that ∠UTX ≅ ∠VTS (angle sum property of triangles).

6. By Angle-Angle (AA) congruence, ∆UTX ≅ ∆VTS.

7. Since corresponding parts of congruent triangles are congruent, we have UX ≅ SV (side UT ≅ side VT).

Therefore, we have proved that UX is congruent (≅) to SV using the information.

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Answer:

y = 15

x = 43

Step-by-step explanation:

x + y = 48

x - 2y = 3

3y = 45

y = 15

x + y = 48

x + 15 = 48

x = 43

1. The smallest critical value for the given hypothesis test is -1.2816.2. The p-value is 0.2148.3. The smallest critical value for the given hypothesis test is 1.796.4. The absolute value of the test statistic is 1.51

1. For a one-tailed hypothesis test with a 10% significance level and 30 degrees of freedom, the smallest critical value is -1.2816.

2. Given the sample data and hypothesis, the appropriate test is a paired t-test for two related samples, where the null hypothesis is that the mean difference is zero. The difference in weight for each subject is (after - before), and the sample mean and standard deviation of the differences are -2.00 and 1.546, respectively.

The t-statistic for this test is calculated as follows:t = (mean difference - hypothesized mean difference) / (standard error of the mean difference)

t = (-2.00 - 0) / (1.546 / √7)

t = -2.74

where √7 is the square root of the sample size (n = 7). The p-value for this test is 0.2148, which is greater than the 0.01 level of significance.

Therefore, we fail to reject the null hypothesis, and we conclude that there is not enough evidence to support the claim that the diet is not effective in reducing weight.

3. To test the claim that blood pressure levels for women vary more than blood pressure levels for men, we need to perform an F-test for the equality of variances. The null hypothesis is that the population variances are equal, and the alternative hypothesis is that the population variance for women is greater than the population variance for men.

The test statistic for this test is calculated as follows:

F = (s1^2 / s2^2)F = (6^2 / 2.2^2)

F = 61.63

where s1 and s2 are the sample standard deviations for women and men, respectively. The critical value for this test, with 8 and 11 degrees of freedom and a 0.05 significance level, is 3.042.

Since the calculated F-value is greater than the critical value, we reject the null hypothesis and conclude that there is enough evidence to support the claim that blood pressure levels for women vary more than blood pressure levels for men.

4. To test the claim that the paired sample data come from a population for which the mean difference is μd = 0, we need to perform a one-sample t-test for the mean of differences. The null hypothesis is that the mean difference is zero, and the alternative hypothesis is that the mean difference is not zero.

The test statistic for this test is calculated as follows:t = (mean difference - hypothesized mean difference) / (standard error of the mean difference)

t = (-0.20 - 0) / (1.465 / √5)t = -0.39

where √5 is the square root of the sample size (n = 5). Since the test is two-tailed, we take the absolute value of the test statistic, which is 1.51 (rounded to two decimal places).

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Answer:

V ≈ 552.9 cm³

Step-by-step explanation:

The volume (V) of a cylinder is calculated as

V = πr²h ( r is the radius and h the height ) , then

V = π × 4² × 11 = π × 16 × 11 = 176π ≈ 552.9 cm³ ( to the nearest tenth )

Answer:

The volume of Coke can is 552.64 cm².

Step-by-step explanation:

Given :

To Find :

Using Formula :

\({\star{\small{\underline{\boxed{\sf{\red{V_{(Can)} = \pi{r}^{2}h}}}}}}}\)

Solution :

Here's the Coke can is in cylindrical form.

So, finding the volume of Coke can by substituting the values in the formula :

\({\dashrightarrow{\pmb{\sf{Volume_{(Can)} = \pi{r}^{2}h}}}}\)

\({\dashrightarrow{\sf{Volume_{(Can)} = 3.14 \times {(4)}^{2} \times 11}}}\)

\({\dashrightarrow{\sf{Volume_{(Can)} = 3.14 \times {(4 \times 4)}\times 11}}}\)

\({\dashrightarrow{\sf{Volume_{(Can)} = 3.14 \times {(16)}\times 11}}}\)

\({\dashrightarrow{\sf{Volume_{(Can)} = 3.14 \times {16}\times 11}}}\)

\({\dashrightarrow{\sf{Volume_{(Can)} = \dfrac{314}{100} \times {16}\times 11}}}\)

\({\dashrightarrow{\sf{Volume_{(Can)} = \dfrac{314 \times 16 \times 11}{100}}}}\)

\({\dashrightarrow{\sf{Volume_{(Can)} = \dfrac{5024 \times 11}{100}}}}\)

\({\dashrightarrow{\sf{Volume_{(Can)} = \dfrac{55264}{100}}}}\)

\({\dashrightarrow{\sf{Volume_{(Can)} \approx 552.64 \: {cm}^{2}}}}\)

\(\star{\red{\underline{\boxed{\sf{Volume_{(Can)} \approx 552.64 \: {cm}^{2}}}}}}\)

Hence, the volume of Coke can is 552.64 cm².

the second one √72= 8.48 and the square root of √83=9.11 pi^2 = 9.86

when you put this in order by the decimal you get

8.48, 8.7, 9.11, 9.25, 9.86 which is really √72, 8.7, √83, 9.25, pi^2

The answer would be 0.5. You're welcome!

The expanded form of the given logarithms (log z²/5) = 2logz + log 5

Four fundamental features are derived directly from the notion that logs are exponents. The first three can be recalled as follows: The log of a product equals the sum of the logs of the elements. A quotient's log is proportional to the difference in between numerator and denominator logs. The log of power is the power multiplied by the log of the base.

Given : log z²/5

Applying the property  (log a/b = log a +log b)

we get:

log z²/5

log z² + log 5

Applying the property

log z²

2 log z

replacing  equation:

log z² + log 5

2logz + log 5

The expanded form of the given logarithms (log z²/5) = 2logz + log 5

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Answer :

3/4.

Explanation

Find the GCD (or HCF) of numerator and denominator

GCD of 45 and 60 is 15

Divide both the numerator and denominator by the GCD

45 ÷ 15

60 ÷ 15

Reduced fraction: 3/4

Therefore, 45/60 simplified to lowest terms is 3/4.

Hi! I hope you are enjoying your day!

In order to simplify this ratio (and 45:60 is a ratio), we should divide both sides of the ratio by 5 (because both 45 and 60 are evenly divisible by 5)

Divide:

9:12

Is the ratio in its simplest form? No.

Why?

Because 9 and 12 can be divided by 3:

3:4

Now the ratio IS in its simplest form.

Hence, the answer is

\(\boxed{\boxed{\bold{3:4}}}\)

Hope everything is clear.

If you have any questions, please comment.

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Answer: 12.57

Step-by-step explanation:

If you're trying to find out what x is then you would have to square root (√) 158 which is 12.57 (2 decimal places)

Answer:

I think this is the estimated answer 12.56980

Step-by-step explanation:

1) The sample space consists of all possible outcomes of coin tosses until the first "H" occurs

2) Probability of each outcome given by (1/2)^(n+1) where n is the number of tails before the first head

The sample space for this experiment is the set of all possible outcomes of the coin tosses until the first "H" occurs. This includes all possible sequences of "T" (tails) and "H" (heads), with the restriction that the first "H" must be the last element in the sequence. For example, some possible outcomes are:

"H" (the first toss is heads)

"TH" (the first heads is on the second toss)

"TTTH" (the first heads is on the fourth toss)

To find the probability law for this experiment, we can use a tree diagram to represent all possible outcomes and their probabilities. At each node in the tree, we branch to represent the two possible outcomes of the next coin toss (heads or tails). The probability of each branch is 1/2, since the coin is fair.

Here is the first level of the tree:

H (probability 1/2)

T (probability 1/2)

If the first toss is heads, we have reached the desired outcome and the experiment ends. If the first toss is tails, we continue branching:

T - H (probability 1/2 * 1/2 = 1/4)

T - T (probability 1/2 * 1/2 = 1/4)

If the second toss is heads, the experiment ends with a total of two tosses. If the second toss is tails, we continue branching:

T - T - H (probability 1/2 * 1/2 * 1/2 = 1/8)

T - T - T (probability 1/2 * 1/2 * 1/2 = 1/8)

We can continue this process to generate the full tree, which has an infinite number of levels (since the experiment could theoretically go on forever). However, we can see that each outcome corresponds to a unique path through the tree, and the probability of that outcome is the product of the probabilities along that path. For example, the outcome "TH" has probability 1/2 * 1/2 = 1/4, while the outcome "TTTH" has probability 1/2 * 1/2 * 1/2 * 1/2 = 1/16.

Therefore, the probability law for this experiment is:

P("H") = 1/2

P("TH") = 1/4

P("TTH") = 1/8

P("TTTH") = 1/16

In general, the probability of the outcome "T^nH" (where there are n tails before the first heads) is (1/2)^{n+1}. The probability of the experiment going on forever (i.e. never getting heads) is 0, since the probability of this outcome is the limit of (1/2)^{n+1} as n approaches infinity, which is 0.

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Answer: The answer is A, the tank starts with 10 gallons of gas.

Answer:

The first one

It shows how much it goes down throughout the journey, starting at 10

Answer:

x = -1.52016

Step-by-step explanation:

Step 1: Write equation

3(2x - 7) = 5(x + 3) + 2x⁷

Step 2: Solve for x

The probability that chloride concentration x will exceed the mean by at least one standard deviation is approximately 0.1587 or 15.87%.

We know that the mean of the blood chloride concentration is 104 mmol/l and the standard deviation is 5 mmol/l. To find the probability that the chloride concentration x will exceed the mean by at least one standard deviation, we need to find the z-score.

The formula for calculating the z-score is:

z = (x - μ) / σ

Where x is the value of interest, μ is the mean and σ is the standard deviation.

In this case, we want to find the probability that x exceeds the mean by at least one standard deviation. This means we need to calculate the z-score for x = 109 mmol/l (the mean plus one standard deviation).

z = (109 - 104) / 5
z = 1

Now we need to find the probability that z is greater than or equal to 1. We can use a z-table or calculator to find this probability. The probability of z being greater than or equal to 1 is approximately 0.1587.

Therefore, the probability that chloride concentration x will exceed the mean by at least one standard deviation is approximately 0.1587 or 15.87%.

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The number of push-ups did sara did during gym class if for every 7 push-ups Dulce can do, Sara can do 6 is 24 push ups.

Number of push ups Dulce can do : number of push ups Sara can do

Let

number of push ups Sara does = x

7 : 6 = 28 : x

7/6 = 28/x

cross product

7 × x = 28 × 6

7x = 168

divide both sides by 7

x = 168/7

x = 24

Therefore, Sara does 24 push ups during the gym class.

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Answer:

2.25 -0.25 increasing (-0.25,2.25)

Step-by-step explanation:

The minimum and maximum values are negative 1/4 and 9/4. In the interval of (0, π/2), the function is decreasing. And the range of the function will be [–1/4, 9/4].

It is a function that repeats itself in a particular time interval.

The equation is given as

y = A sin (ωx + Ф) + C

Where A is the amplitude, ω is the frequency, Ф is the phase difference, and C is the constant.

The function is given below.

f(x) = (5/4) sin(x) + 1

Compare the function with standard equation.

A = 5 / 4

ω = 1

Ф = 0

C = 1

Then the maximum value of the function at sin x = 1, will be

Maximum value = 5/4 + 1

Maximum value = 9/4

Then the minimum value of the function at sin x = –1, will be

Minimum value = –5/4 + 1

Minimum value = –1/4

In the interval of (0, π/2), the function is decreasing.

And the range of the function will be [–1/4, 9/4].

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The height of the room is 5 m.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Length = 7 m

Width = 2 m

Height = x

Four walls of a room will have,

Two walls of length x height.

Two walls of Width x height.

Now,

Area four walls of the room = 90 m

2 (length x height) + 2 (Width x height) = 90

2 (7x) + 2 (2x) = 90

14x + 4x = 90

18x = 90

x = 5

Thus,

Height of the room = 5 m.

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Answer: 743.30343766 . . . ft

Round it to whatever place your teacher requires it to be at.

Step-by-step explanation: So, this question can be treated as one in which you need to find the hypotenuse. If you cut the soccer field diagonally, the length and width are still the same. The two legs of our triangle are 700 ft and 250 ft. The formula for finding the hypotenuse is a²+b²=c². Input the numbers, and it becomes 700²+250²=c². 700² is 490,000 and 250² is 62,500. 490,000 + 62,500 = 552,500. This means that 552,500 is c², and in order to find c, or the hypotenuse/diagonal, we need to find the square root of 552,500. The square root of 552,500 is 743.3034376 . . . , which you can round to whatever place you need it to be at.

Answer:

654 grams

Step-by-step explanation:

When you set up this equation you want the number of grams you start with, 2616, and the factor by which it is decreasing, which is half, or 1/2. Because the half life is 11 days, but you want to find the amount left over after 22 days, you can make 22/11 as the exponent on the 1/2. The equation should look like this : 2616(1/2)^22/11. With these kinds of equations you always want to multiply the starting value by the factor of increase/decrease, and raise that factor to the time eclipsed divided by the set time(like the 11 day half life).

Answer:

Area

Step-by-step explanation:

That's the definition of area.

The 90% confidence interval for the average speed of all the cars passing through the intersection is (41.29, 42.71) miles per hour.

To calculate the confidence interval, we can use the formula:

Confidence interval = Sample mean ± (Critical value * Standard error)

Given that the sample mean is 42 miles per hour and the standard deviation is 4.2 miles per hour, we need to determine the critical value and the standard error.

Since we have a sample size of 85, we can use the t-distribution with (n-1) degrees of freedom to find the critical value. With a 90% confidence level, the corresponding critical value for a two-tailed test is approximately 1.66.

The standard error is calculated as the standard deviation divided by the square root of the sample size:

Standard error = (Standard deviation) / √(Sample size)

Standard error = 4.2 / √85 ≈ 0.456

Now we can plug in the values into the confidence interval formula:

Confidence interval = 42 ± (1.66 * 0.456)

Confidence interval ≈ (41.29, 42.71)

Therefore, the 90% confidence interval for the average speed of all the cars passing through the intersection is (41.29, 42.71) miles per hour.

Based on the given data and calculations, we can conclude that with 90% confidence, the average speed of all the cars passing through the intersection falls within the range of 41.29 to 42.71 miles per hour.

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The correct option is "the standard error is the standard deviation of the sampling distribution." Correct option is A.

The standard error is a measure of the variability of a sampling distribution, which is the distribution of sample statistics (e.g., mean, proportion) that would be obtained from multiple random samples of the same size from the same population.

The standard error represents the standard deviation of the sampling distribution, and it provides a measure of the precision of the sample statistic in estimating the population parameter.

The standard error is not the same as the standard deviation of the sample, which is a measure of the variability of the individual observations in the sample.

The standard deviation of the sample is typically used to estimate the standard deviation of the population, while the standard error is used to estimate the variability of the sample statistic and to construct confidence intervals or perform hypothesis tests.

While the other options are related to the concept of the standard error, they are not equivalent or fully accurate descriptions of what the standard error represents.

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Complete question is:

What is the standard error?

group of answer choices

A. the standard error is the standard deviation of the sampling distribution

B. the standard error is a measure of how representative a sample statistic is likely to be of the population parameter.

C. the standard error is calculated using the standard deviation of the sample all of the options describe the standard error.

One saturday omar collected from his newspaper customers twice as many dollar bills as fives and one fewer ten than fives. if omar collected $58, then he must have collected 3 fives, 2 tens, and 23 ones.

To solve this problem, let's break it down step-by-step:
1. Let's assign variables to the number of fives, tens, and ones Omar collected. We'll call the number of fives "x", the number of tens "y", and the number of ones "z".

2. According to the problem, Omar collected twice as many dollar bills as fives. This means the number of dollar bills (which includes fives, tens, and ones) is 2x.

3. The problem also states that Omar collected one fewer ten than fives. So, the number of tens is x - 1.

4. Now we can create an equation based on the information given. The total amount of money Omar collected is $58. We can express this as an equation: 5x + 10y + z = 58.

5. Substituting the expressions we found earlier for the number of dollar bills and tens into the equation, we have: 5x + 10(x - 1) + z = 58.

6. Simplifying the equation, we get: 5x + 10x - 10 + z = 58.

7. Combining like terms, we have: 15x + z - 10 = 58.

8. Rearranging the equation, we get: 15x + z = 68.

9. Now, let's find possible values for x, y, and z that satisfy this equation. We know that x, y, and z must be positive integers.

10. By trial and error, we can find that when x = 3, y = 2, and z = 23, the equation is satisfied: 15(3) + 2(10) + 23 = 68.

Therefore, Omar collected 3 fives, 2 tens, and 23 ones.

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The number of additional gifts Jeff can buy with the remaining cost is 1.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

As per the given,

Total cost = $15 + $20 = $35

Total spent = $50

Remaining = $50 - $35 = $15

Since one gift cost $10

Thus, 15/10 = 1.5 since the number of gifts will be the whole number so it will be round to bottom 1 gift.

Hence "With the money still available, Jeff can purchase 1 more present".

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Answer:

1.1. 3(2a-7)

1.2. 3x(2x+3)

Step-by-step explanation:

Put the common factor on the outside of the parentheses.

1.1. 6a-21

The lowest common factor for 6a and -21 is 3.

     3(2a-7)

1.2. \(6x^{2} +9x\)

The lowest common factor for \(6x^{2}\) and 9x is 3x.

      3x(2x+3)

Answer:

x=7/10

Step-by-step explanation:

Because this is a square, we know that all of the sides are equal.

Thus, we know that 6x-1=4x+6.

We can further use Algebra and subtract by 4x on both sides.

Now, we have 10x-1=6.

Then, we can add 1 to both sides, and get 10x=7.

Lastly, let's divide both sides by 10 to isolate x, getting x=7/10, or x=0.7

Using the formula °F = 1.8°C +32°, The temperature in Degrees Celsius of an oven that is 500°F is 260°C.

For everyday purposes, Fahrenheit is used in the United States, its territories, and related states (all of which are covered by the U.S. National Weather Service), as well as in Liberia, the Cayman Islands, and other places. For instance, temperatures for freezing, cooking, and other conditions are typically given in degrees Fahrenheit in the United States.

On the Celsius scale, one of the two temperature scales used in the International System of Units along with the Kelvin scale, the unit of temperature is the degree Celsius. The term "degree Celsius" can be used to describe either a specific temperature on the Celsius scale or a measurement of the difference between two temperatures.

Here,

°F=1.8°C+32°

500°F=1.8°C+32°

1.8°C=468°F

°C=468/1.8

°C=260°C

The temperature in Degrees Celsius of an oven that is 500°F is 260°C by using the formula °F = 1.8°C +32°.

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