The sides of a triangle have lengths 3, 25, and 27. What kind of triangle is it ?

No, the line x=1-2t, y=2+5t, z=-3t is not parallel to the plane 2x+y-z=8 as their dot product is not zero.

To determine if the line x = 1 - 2t, y = 2 + 5t, z = -3t is parallel to the plane 2x + y - z = 8, we can find the direction vector of the line and check if it is orthogonal to the normal vector of the plane.

The direction vector of the line is given by the coefficients of t in each component, which is (-2, 5, -3).

The normal vector of the plane is given by the coefficients of x, y, and z in the plane's equation, which is (2, 1, -1).

To check if the direction vector is orthogonal to the normal vector, we can take their dot product and see if it is zero:

(-2, 5, -3) * (2, 1, -1) = -4 + 5 + 3 = 4

Since the dot product is not zero, the direction vector of the line and the normal vector of the plane are not orthogonal, which means the line is not parallel to the plane.

The line x = 1 - 2t, y = 2 + 5t, and z = -3t is not parallel to the plane 2x + y - z = 8, hence the answer is no.

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The function that is linear is the function that is a straight line

A linear function can be identified on a graph by its shape.

A linear function will always have a straight line.  So, if the graph of several functions, then the linear function would be a straight line.

To confirm that it is a linear function, you can check if it has the form y = mx + b, where m and b are constants.

In this form, m represents the slope of the line, which is a measure of how steep the line is.  and b is the y-intercept

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The argument is not valid.

The argument form is: p ∧ ∼ q → r, p ∨ q, q → p, therefore r. We can use the truth table to determine whether this argument is valid or invalid. Here is the annotated truth table:


 
   p
   q
   ∼q
   p ∧ ∼q
   p ∨ q
   p ∧ ∼q → r
   q → p
   r
 
 
   T
   T
   F
   F
   T
   T
   T
   T
 
 
   T
   F
   T
   T
   T
   T
   T
   T
 
 
   F
   T
   F
   F
   T
   T
   F
   F
 
 
   F
   F
   T
   F
   F
   T
   T
   F
 

From the truth table, we can see that the conclusion r is not always true, even when all the premises are true. For example, in the third row of the table, all the premises are true, but the conclusion is false. This means that the argument is invalid. The truth table supports this conclusion because it shows that there are cases where the premises are true but the conclusion is false. Therefore, the argument is not valid.

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Step-by-step explanation:

the whole circle of B including the Intersection part of A and B is shaded here...

I hope the image helps you understand better

Answer:

20

Step-by-step explanation:

'of' means multiplication

'is' means equals

1.5x = 30

x = 30 ÷ 1.5

x = 20

Answer:

Step-by-step explanation:

Answer:

m<2 = 47.5 degrees

m<3 = 42.5 degrees

m<4 = 42.5 degrees

Step-by-step explanation:

<1 = <2 Given

<1 = 47.5 Given. <2 = 47.5

<1 and <3 are complementary angles. Given

<1 + <3 = 90 degrees

<3 = 90 - 47.5 = 42.5 degrees

<4 = <3

The speed of sound is about 331.5 m/s at 0 degree-Celsius. The speed of sound increases by 0.6 meters per second (m/s) for every degree-Celsius increase in temperature.

The standard deviation of quiz scores is 0.

To find the standard deviation:

Therefore, the standard deviation of quiz scores is 0.

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Answer:

(1,8)

Step-by-step explanation:

please mark me as brainliest thank you

If we compare the p value and the significance level provided we see that pv > α so on this case we have enough evidence in order to FAIL reject the null hypothesis at the significance level provided. And that means that the population variance is not significantly higher than 0.0004, so there is no a violation of the specifications.

A chi-square test is "used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value"

n = represent the sample size

α=  represent the confidence level

s² = represent the sample variance obtained

σ =  represent the value that we want to test

Null and alternative hypothesis

On this case we want to check if the population variance specification is violated, so the system of hypothesis would be:

Null Hypothesis: σ² ≤ 0.004

Alternative hypothesis: σ² > 0.004

Calculate the statistic

X = ((n - 1)/σ²)s²

For this test we can use the following statistic:

X² = ((30 - 1)/0.0004)0.0005

And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.

Calculate the p value

In order to calculate the p value we need to have in count the degrees of freedom , on this case 29. And since is a right tailed test the p value would be given by:

Pv = P(X² > 36.25) = 0.1664

Therefore, If we compare the p value and the significance level provided we see that pv > α so on this case we have enough evidence in order to FAIL reject the null hypothesis at the significance level provided. And that means that the population variance is not significantly higher than 0.0004, so there is no a violation of the specifications.

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Answer: 33

Step-by-step explanation:

Answer:

Step-by-step explanation:

33

Answer:

Literally nothing.

Step-by-step explanation:

Lol

Given the function p(x)=6x+2, p(-2) is -10 while p(4) is 26, this shows that value of p(-2) is smaller than the value of p(4). The correct option is B.

A function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). It is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.

p(x)=6x+2

for p(-2)

p(-2) = 6(-2) + 2

p(-2) = -12 + 2

p(-2) = -10

for p(4)

p(4) = 6(4) + 2

p(4) = 24 + 2

p(4) = 26

p(-2) < p(4)

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Answer:

(B) "The value of p(-2) is smaller then the value of p(4)" is True

Step-by-step explanation:

p(x)=6x+2

p(-2) = 6*(-2)+2

p(-2) = -12+2

p(-2) = -10

p(4) = 6*(4)+2

p(4) = 26

====

p(-2) = -10

p(4) = 26

===

(A) The value of p(-2) is larger then the value of p(4).   False

(B) The value of p(-2) is smaller then the value of p(4).  True

(C) The value of p(-2) is the same as the value of p(4).  False

(D) The values of p(-2) and p(4) cannot be compared.   False

If it is assumed that all 52 5 poker hands are equally likely, the probability of being dealt a flush is 0.001981

Flush means all 5 cards are of the same suit.

Now, we need to select one suit out of 4 which can be done in ⁴C₁ ways.

Now, when the suit is selected, we have to select 5 cards from that specific suit. This can be done in ¹³C₅ ways

In the game of poker, there are ⁵²C₅ possible hands.

So, the probability of a flush is given by:

              P = (⁴C₁ × ¹³C₅)/⁵²C₅

              P = (4 × 1287)/2598960

              P = 5148/2598960

              P = 0.001981 or 1.981 × 10⁻³ or 0.1981 %

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The required confidence interval is,

⇒ CI = (0.628, 0.797)

According to the given information,

We can use a formula to calculate the confidence interval,

⇒ CI = p ± z  (√(p(1-p)/n))

Where,

p = sample proportion = 67/94 = 0.7128

z = z-score corresponding to a 90% confidence level = 1.645 (you can find this value on a z-table)

n = sample size = 94

So put the values, we get,

⇒ CI = 0.7128 ± 1.645 (√((0.7128 (1 - 0.7128))/94))

Simplifying this formula, we can get,

⇒ CI = 0.7128 ± 0.0846

Therefore, the 90% confidence interval for the true proportion of all adults in the town who have health insurance is,

⇒ CI = (0.6282, 0.7974)

In Interval Notation with decimal rounded to the thousandths,

⇒ CI = (0.628, 0.797)

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The value of x is: x = 35.57.

Here, we have,

given that,

from the given diagram, we get,

it is a right angle triangle,

base = x

hypotenuse = 37

and angle = 16°

now, we know that,

cos θ = adjacent / hypotenuse

so, we get,

cos 16° = x/37

The value of cos 16° is equal to the x-coordinate (0.9613).

∴ cos 16° = 0.9613.

=> 0.9613 = x/37

=> x = 35.57

Hence, The value of x is: x = 35.57.

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Step-by-step explanation:

Hey there!

Given;

4(X+1) -3 and 4x+1.

No, they are equivalent.

Reason:

Solving 1st expression.

4(x+1) = 4x + 4 - 3

Now, next expression is: 4x+1.

So, 4x + 4 = 4x+1

So, they are equivalent to eachother.

Hope it helps...

is 4(x+1) - 3 and 4x + 1 equivalent and why?

Step-by-step explanation:

Hey there!

Given;

4(X+1) -3 and 4x+1.

No, they are equivalent.

Reason:

Solving 1st expression.

4(x+1) = 4x + 4 - 3

Now, next expression is: 4x+1.

So, 4x + 4 = 4x+1

So, they are equivalent to eachother.

Hope it helps...

Based on the given information, g(x) has a larger average rate of change than f(x) = 2^x over that interval.

What is a function?

A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.

To determine which function has a larger average rate of change between x=2 and x=3 than f(x) = 2^x, we need to find the average rate of change of f(x) over that interval first.

The average rate of change of f(x) between x=a and x=b is given by:

(f(b) - f(a))/(b - a)

In this case, a=2 and b=3, so we have:

(f(3) - f(2))/(3 - 2)

= (2^3 - 2^2)/(1)

= (8 - 4)/(1)

= 4

So the average rate of change of f(x) between x=2 and x=3 is 4.

Now we need to find another function whose average rate of change over the interval (2, 3) is greater than 4.

One such function could be g(x) = 3x - 4. To find its average rate of change over the interval (2, 3), we have:

(g(3) - g(2))/(3 - 2)

= (3(3) - 4) - (3(2) - 4))/(1)

= (5)/(1)

= 5

Since the average rate of change of g(x) over (2, 3) is greater than 4, we can conclude that g(x) has a larger average rate of change than f(x) = 2^x over that interval.

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To write 45 + 3/10 + 8/1000 as a decimal, we need to convert the fractions 3/10 and 8/1000 to their equivalent decimal form and then add all three numbers. The result is 45.308, which can be simplified to 45.31 by rounding to the nearest hundredth.

Explanation:

To convert 3/10 to a decimal, we divide 3 by 10, which gives 0.3. To convert 8/1000 to a decimal, we divide 8 by 1000, which gives 0.008. We can then add 45, 0.3, and 0.008 to get:

45 + 0.3 + 0.008 = 45.308

To simplify this result to the nearest hundredth, we look at the digit in the third decimal place (8) and round the digit in the second decimal place (0) up to 1 if the third decimal place is 5 or greater. In this case, the third decimal place is 8, which is greater than 5, so we round up to get:

45.31

Therefore, 45 + 3/10 + 8/1000 is equal to 45.31 when written as a decimal.

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Answer:

answer: 9/40

Step-by-step explanation:

18 ÷ 2 = 9 and 80 ÷ 2 = 40 and you can't go any further so 9/40 is the answer.

The probability that the child exhibits the disease is 18.75%

To determine the probability that the child exhibits the disease, we need to first find the probability of the child inheriting the disease-causing genotype and then multiply it by the penetrance of the disease.

Step 1: Determine the genotype probabilities
Since both parents are heterozygotes, their genotypes are Gg. Using a Punnett square, we can determine the probabilities of the child's possible genotypes:

Parent 1: G | g
Parent 2: G | GG | Gg
           g | Gg | gg

The child's possible genotypes and their probabilities are:
- GG: 1/4 (25%)
- Gg: 1/2 (50%)
- gg: 1/4 (25%)

Step 2: Determine the probability of the child exhibiting the disease
The disease is caused by homozygosity for the g allele, meaning the child must have the gg genotype to potentially have the disease. The probability of the child inheriting the gg genotype is 1/4 (25%).

Step 3: Factor in the penetrance of the disease
Since the penetrance of the disease is 75%, this means that 75% of individuals with the gg genotype will exhibit the disease. To find the probability of the child exhibiting the disease, multiply the probability of inheriting the gg genotype (1/4) by the penetrance (75%):

(1/4) * (75%) = 0.25 * 0.75 = 0.1875

Therefore, the probability that the child exhibits the disease is 18.75%.

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Answer:

\( \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- 2x {e}^{x} + 2 e^{x} + \rm C\)

Step-by-step explanation:

we want to integrate the following integration:

\( \displaystyle \int {x}^{2} \cdot {e}^{x} dx\)

notice that, the integrand is in the multiplication of two different function in that case we can consider integration by parts given by:

\( \rm \displaystyle \int u \cdot v \: dx = u \int vdx - \int u' \left( \int v dx \right)dx\)

where u' can be defined by the differentiation of u

now we have to choose our u and v

which can be chosen by using the guideline:ILATE Inverse trig. , Logarithm, Algebraic expression, Trigonometry, Exponent.

since x comes first thus,

\( \displaystyle u = {x}^{2} \quad\text{and} \quad v = {e}^{x} \)

by figuring out the defferentiation of u,we acquire:

\( \displaystyle u' = 2x\)

altogether we get:

\( \rm \displaystyle \int {x}^{2} \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \int 2x \left( \int {e}^{x} dx \right)dx\)

by figuring out the parentheses integration

we get:

\( \rm \displaystyle \int x^2 \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \int2x \cdot {e}^{x} dx\)

now we again have integration of two different functions so let's choose our u and v once again which can be done using the guideline

\( \displaystyle u = 2x \quad\text{and} \quad v = {e}^{x} \)

by figuring out the defferentiation of u

we acquire:

\( \displaystyle \: u' = 2\)

altogether we get:

\( \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \left( 2x \int{e}^{x} dx- \int2 \left( \int{e}^{x}dx \right) dx \right)\)

by solving parentheses we get

\( \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \left( 2x {e}^{x} - 2 e^{x} dx \right)\)

by figuring out the integral we get:

\( \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- \left( 2x {e}^{x} - 2 e^{x} \right)\)

remove parentheses:

\( \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- 2x {e}^{x} + 2 e^{x} \)

at last we of course have to add constant of integration:

\( \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- 2x {e}^{x} + 2 e^{x} + \rm C\)

and we are done!

Answer:

\(\displaystyle \int {x^2e^x} \, dx = e^x(x^2 - 2x + 2) + C\)

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           \(\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)\)

Basic Power Rule:

Integration

Integration by Parts:                                                                                               \(\displaystyle \int {u} \, dv = uv - \int {v} \, du\)

Step-by-step explanation:

*Note:

The answer below me is correct, but there is a simpler method of obtaining the answer.

Step 1: Define

Identify

\(\displaystyle \int {x^2e^x} \, dx\)

Step 2: Integrate

Use tabular integration.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

The inequality in a standard form that describes this situation is,

52000x + 84000y < 830000.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

From the given information, x = the number of junior programmers y = the number of senior programmers,

The inequality that represents the situation is,

52000x + 84000y < 830000.

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Answer:

$90.95

Step-by-step explanation:

$25+$60=$85

$85x0.07=$5.95

$85+$5.95=$90.95

Answer: $90.95

60+25= 85

85*.07= 5.95

85+5.95= 90.95

==========================================================

Explanation:

Check out the diagram below to see what's going on.

Use the pythagorean theorem to find b

\(a^2 + b^2 = c^2\\\\b = \sqrt{c^2 - a^2}\\\\b = \sqrt{9^2 - (8.2)^2}\\\\b = \sqrt{81 - 67.24}\\\\b = \sqrt{13.76}\\\\b \approx 3.709 447\\\\b \approx 3.7\\\\\)

The length is roughly 3.7 feet.

a) The selling price of the skis is $79.80.

b) The final price is 140% of the original price.

c) The percent increase from the original price to the final price is 40%.

a) Calculation of selling price:

Markup rate is 40%

Original cost = $57

Selling price = (100% + Markup percentage) × Original cost

Selling price = (100% + 40%) × $57

Selling price = 1.4 × $57

Selling price = $79.80

b) Calculation of percentage of the original price that is the final price

Percentage of original price that is the final price = (Final price / Original price) × 100%

Percentage of original price that is the final price = ($79.80 / $57) × 100%

Percentage of original price that is the final price = 140%

c) Calculation of the percentage increase

Percentage increase = (Final value − Initial value) / Initial value × 100%

Percentage increase = ($79.80 − $57) / $57 × 100%

Percentage increase = $22.80 / $57 × 100%

Percentage increase = 40%

Therefore, The store charges $79.80 for the skis. The final price is 140% of the original price and the percent increase from the original price to the final price is 40%.

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Answer: Jamal

Step-by-step explanation:

7/9 = 0.777...

5/8 = 0.625

Therefore, Jamal has a higher probability of making it in.

Answer:

Jamal

Step-by-step explanation:

7/9= 0.77

5/8= 0.62

Jamal has a higher probability of making it

The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:

"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."

The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.

Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.

In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.

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The product of the expressions (x⁵y³z²) and (x⁴y³z⁶) is equivalent to the expression x⁹y⁶z⁸. Then the correct option is A.

The equivalent is the expressions that are in different forms but are equal to the same value.

The expression is given below.

(x⁵y³z²) and (x⁴y³z⁶)

Then the product of the expression will be

⇒ (x⁵y³z²) (x⁴y³z⁶)

⇒ x⁵x⁴y³y³z²z⁶

⇒ x⁵⁺⁴y³⁺³z²⁺⁶

⇒ x⁹y⁶z⁸

Then the correct option is A.

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