Which expression is equivalent to x² - 4x - 45?
А
(x - 9)(x - 5)
B
(x + 9)(x+5)
(20 +9)(x - 5)
D
(x - 9)(x+5)

The problem provides the information:

3 x + 5 y = 11

and x y = 2

Asking to find the value of 9 x^2 + 25 y^2

so we proceed to recall what the square of a binimial of the following form is:

So, we see that the square of the quantity: (3 x + 5 y) which from the information given equals 11^2 = 121, must equal the expression:

9 x^2 + 25 y^2 + 30 x y.

then we write the following equation making both parts equal:

Therefore the value of 9 x^2 + 25 y^2 = 61

Answer:

C

Step-by-step explanation:

430 feet above sea level

Answer:

C. 430 feet above sea level

No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.

A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.

The distributive property states that for any real numbers a, b, and c:

a × (b + c) = (a × b) + (a × c).

When working with fractions, we can apply the distributive property as follows:

Let's consider the expression: a × (b/c).

We can rewrite this as: (a × b)/c.

Now, let's distribute the 'a' to 'b' and 'c':

(a × b)/c = (a/c) × b.

In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.

Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.

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Answer:

  x^0

Step-by-step explanation:

1/x = x^-1

For x > 1, this fraction is less than 1, so will be smaller than x^0, which is 1.

x^0 is bigger

Answer:

.15

Step-by-step explanation:

Answer:

.15, 3/20

Step-by-step explanation:

Answer:

y=-5x thats it so ype it in ir whatevet

Answer:

12.6 units.

Step-by-step explanation:

According to cosine formula:

\(a^2=b^2+c^2-2bc\cos A\)

Using cosine formula in triangle STU, we get

\((SU)^2=(ST)^2+(TU)^2-2(ST)(TU)\cos T\)

\(t^2=(5)^2+(15)^2-2(5)(15)\cos (53^{\circ})\)

\(t^2=25+225-150(0.60)\)

\(t^2=160\)

Taking square root on both sides.

\(t=\sqrt{160}\)

\(t\approx 12.6\)

Therefore, the value of t is 12.6 units.

Answer:

Step-by-step explanation:

You want an inequality relating the number of 250 lb refrigerators (x) and the number of 425 lb pianos (y) a truck with a 5900 lb load limit can carry. And you want to know if 12 refrigerators and 8 pianos will overload the truck.

The weight of x refrigerators will be 250x. The weight of y pianos will be 425y. Then the restriction on the total weight is ...

  250x +425y ≤ 5900 . . . . . . the load limit of the truck

The weight of 12 refrigerators and 8 pianos will be ...

  250·12 +425·8 = 3000 +3400 = 6400 . . . . pounds

This weight will overload the truck.

__

Additional comment

The graph shows the point (12, 8) is not in the solution space of the inequality. Hence the truck will be overloaded with that load.

<95141404393>

The sampling distribution of the sample mean diameter (X) for a random sample of n = 16 rings is centered at the population mean of 16 cm. This means that on average, the sample mean diameter will be equal to the population mean. The standard deviation of the X distribution can be calculated using the formula σ/√n, where σ is the population standard deviation and n is the sample size. In this case, the population standard deviation is given as 0.08 cm and the sample size is 16. Therefore, the standard deviation of the X distribution is 0.02 cm.

The sampling distribution is important in statistical analysis as it helps to determine the probability of obtaining a particular sample mean. It also allows us to estimate the true population mean and evaluate the effectiveness of statistical inferences. In this case, we can use the sampling distribution to determine the probability of obtaining a sample mean diameter that is different from the population mean of 16 cm. With a standard deviation of 0.02 cm, we can expect that the sample means will be relatively close to the population mean, with most falling within a few standard deviations from the mean.

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The total price of the bicycle in Pierce county is $4136.24

An equation shows the relationship between two or more variables and numbers.

Let P represent the total price after taxes. The tax rate is 10.3% and the price of the bicycle is $3749.99. Hence:

Tax = 10.3% of $3749.99 = 0.103 * 3749.99 = $386.25

The total price (P) is:

P = $3749.99 + Tax = $3749.99 + $386.25

P = $4136.24

Therefore, the total price of the bicycle in Pierce county is $4136.24

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A cargo ship left port A and is headed across the ocean to shipping port B. After one month, the ship stopped at a refueling station along a path described by a vector with components 〈14, 23〉. The characteristics of the vector representing the path of the ship are "components: 〈7, 11.5〉, magnitude: 13.46".

After another month, on the same path, the ship reached port B, twice the distance from port A as the fueling station. The distance between A and the fueling station is x units.

Then, the distance between B and the fueling station is 2x units.AB = 2x units. The fueling station is located at 〈14, 23〉. And A is located at (0, 0)Now we can calculate the distance between A and the fueling station using the distance formula.= √[(14 - 0)² + (23 - 0)²]= √(196 + 529)= √725= 26.92 approx.

After another month, on the same path, the ship reached port B, twice the distance from port A as the fueling station. The distance between A and the fueling station is 26.92 units. Then, the distance between B and the fueling station is 2 × 26.92 = 53.85 units.

Now we can calculate the vector AB using the below formula: AB = OB - OAwhere, OA = (0, 0)OB = (7, 11.5)

So, AB = OB - OA= (7, 11.5) - (0, 0)= (7, 11.5)

Magnitude of vector AB = √(7² + 11.5²)= √(49 + 132.25)= √181.25= 13.46 approx.

So, the correct answer is "components: 〈7, 11.5〉, magnitude: 13.46".

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Answer:

4x+3y=6

Step-by-step explanation:

hope this helps

Answer:

xeR meaning interval notation (A set of values between two end points).

Step-by-step explanation:

You didn't say what to solve for, so I solved for x and got that.^

Hopefully that helps.

The p-value for this test is approximately 0.0307.

To find the p-value for the hypothesis test, you can use a standard normal distribution table or a calculator.

Given that the z-test statistic is 1.88, you want to find the probability of obtaining a z-score greater than or equal to 1.88 (since it is a one-tailed test).

Using a standard normal distribution table, you can find the corresponding area under the curve.

The area to the left of 1.88 is 0.9693. Since the test is one-tailed, subtracting this value from 1 gives you the p-value:

p-value = 1 - 0.9693 = 0.0307.

Therefore, the p-value for this test is approximately 0.0307.

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Answer:

Father's age = 65 years

Step-by-step explanation:

Let the age of father = x years

Age of mother           = (x - 4) years

\(\sf Average = \dfrac{Sum \ of \ all \ the \ data}{number \ of \ data}\\\\\boxed{\text{Sum of all data =average * number of data}}\)

  Average age of six children =  19 years  

       Sum of age of 6 children = 19 *6 = 114 years      

Average of all 8 members = 30 years

Sum of age of all members = 30*8 = 240 years

sum of age of 6 children + father's age + mother's age = sum of all age of members

114 + x + x -4  = 240

        110 + 2x = 240

                  2x = 240 -110

                  2x = 130

                    x = 130/2

                    x = 65 years

Father's age = 65 years

Answer:

okay, but what is the equation?

Answer:

Alright Ima need the question

Step-by-step explanation:

The most effective design to test the effects of the new weight loss program would be a randomized block design experiment.

A randomized block design experiment would be the most effective in this scenario because it allows for the control of potential confounding variables, such as gender, while also incorporating randomization.

1. Gender Division: The researchers first divide the participants into groups based on gender. This ensures that there is a balanced representation of both males and females in the study.

2. Random Assignment: Within each gender group, participants are randomly assigned to either the treatment group or the control group. Random assignment helps minimize any systematic differences between the groups, ensuring that any observed effects can be attributed to the weight loss program rather than other factors.

3. Blocking: Gender is considered a blocking factor in this design. By blocking, the researchers ensure that each treatment group and control group includes an equal number of males and females. This helps control for any potential differences between genders that could influence the outcome.

4. Control Group: The control group serves as a baseline comparison for the treatment group. Participants in the control group do not receive the weight loss program but instead receive a placebo or standard care. This allows for a comparison of the effects between the treatment and control groups.

5. Data Analysis: The data collected from this design can be analyzed using appropriate statistical tests, such as t-tests or analysis of variance (ANOVA), to determine if the weight loss program has a significant effect on the outcome variable.

Overall, a randomized block design experiment is the most effective approach in this scenario as it incorporates randomization, controls for potential confounding variables (gender), and allows for a comparison between treatment and control groups.

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The evaluated lateral surface area is 261.8 square meters, under the condition that the base length is 20 m and height is 13 m.

The lateral surface area of a cylinder is given by the formula 2πrh
Here,
r = radius of the base
h = height of the cylinder.
For the given case, the base length is 20 m and height is 13 m. Then the base length is stated  instead of the radius, we have  to evaluate the radius first.
The radius of a cylinder can be found applying the formula r = l/2π
Here,
l = base length.
So, staging l = 20 m
, we get
r = 20/(2π)
≈ 3.18 m
Now that we have received the radius and height, we can evaluate the lateral surface area applying the formula mentioned above.
Staging
r = 3.18 m
h = 13 m,
we get:
Lateral surface area
= 2πrh
≈ 261.8 m²
Then, the lateral surface area of the given cylinder is approximately 261.8 square meters.
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Answer:Sam surveyed his classmates to find out if they played a sport after school or practiced in the

school band

- 14 of his classmates played a sport

- of those 14 who played, 5 participated in the school band

- 8 students played in the school band, and out of those 8, 3 did not play sports

- there were 10 students who did not play a sport nor participate in the school band

Create a two way table to represent the data and answer the following questions

Step-by-step explanation:

Here is a two-way table that represents the given data:

Look at the pic

To create this table, we first divided the students into two categories: those who play a sport and those who do not. Then, we further divided each category into those who play in the school band and those who do not.

From the table, we can answer the following questions:

How many students did Sam survey in total?

To find the total number of students surveyed, we can add up the values in the table:

14 + 5 + 3 + 9 + 10 = 41

Therefore, Sam surveyed a total of 41 students.

How many students played a sport but did not participate in the school band?

From the table, we can see that 14 students played a sport, and 5 of those also participated in the school band. Therefore, the number of students who played a sport but did not participate in the school band is:

14 - 5 = 9

So, 9 students played a sport but did not participate in the school band.

How many students did not play a sport but participated in the school band?

From the table, we can see that 8 students played in the school band, and 3 of those did not play a sport. Therefore, the number of students who did not play a sport but participated in the school band is:

8 - 3 = 5

So, 5 students did not play a sport but participated in the school band.

Hope this helps <3

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The vertex form of a quadratic function is given by:

�

(

�

)

=

�

(

�

−

ℎ

)

2

+

�

f(x)=a(x−h)

2

+k

where $(h, k)$ is the vertex of the parabola.

Substituting the given vertex $\left(-2,\ -6\right)$, we get:

�

(

�

)

=

�

(

�

−

(

−

2

)

)

2

−

6

f(x)=a(x−(−2))

2

−6

Simplifying:

�

(

�

)

=

�

(

�

+

2

)

2

−

6

f(x)=a(x+2)

2

−6

To find the value of $a$, we use the fact that the function passes through the point $\left(-1,\ 2\right)$:

2

=

�

(

−

1

+

2

)

2

−

6

2=a(−1+2)

2

−6

Solving for $a$:

\begin{align*}

2 + 6 &= a(1)^2 \

a &= 8

\end{align*}

Therefore, the quadratic function in vertex form that satisfies the given conditions is:

�

(

�

)

=

8

(

�

+

2

)

2

−

6

f(x)=8(x+2)

2

−6

When we express the equation 2x - y = 12 in slope intercept form, the result obtained is y = 2x - 12 (2nd option)

The slope intercept form for an equation is written as illustrated below:

y = mx + c

Where

With the above information, we can obtain the slope intercept form of the equation. Details below:

2x - y = 12

Rearrange to make y the subject of the expression, we have

2x = 12 + y

y = 2x - 12

Thus, we can conclude that the equation in the slope intercept form is

y = 2x - 12 (2nd option)

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Complete question:

Given the equation 2x - y = 12, which equation is written in slope intercept form?

y = -2x + 12

y = 2x - 12

y = 2x + 12

y = -2x - 12

Answer:

3x + 12 + x = 180

4x +12 = 180

4x = 168

x = 42

(I'm guessing you're in a different timezone than I am because it's already 3:35 here)

Answer:

  h = 6, k = 6.5

Step-by-step explanation:

The segment marked h is half the length of the one marked 3h-6.

  2h = 3h -6

  6 = h . . . . . . . add 6-2h

__

The segment marked k is half the length of the one marked 2h+1.

  2k = 2(6) +1

  k = 13/2 = 6.5 . . . . divide by 2

The values of h and k are 6 and 6.5, respectively.

the equilibrium pressure of HBr is 0.0744 atm (to three decimal places).

The equilibrium pressure of HBr can be calculated using the following expression:

K = \((P(HBr))^2 / (P(H2) x P(Br2))\)

Rearranging this expression, we get:

P(HBr) = \(\sqrt {(K x P(H2) x P(Br2))}\)

Substituting the given values, we get:

P(HBr) = \(\sqrt {(0.00550 x 1.000 atm x 1.000 atm)}\) = 0.0744 atm

Therefore, the equilibrium pressure of HBr is 0.0744 atm (to three decimal places).

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The likelihood that the player's average will be.310 or higher during the following 100 at-bats is. 9267

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The likelihood of obtaining at least 31 hits in 100 at-bats when the likelihood of getting a hit in each at-bat is.300 must be taken into account in order to calculate the likelihood that the player's average during the subsequent 100 times at bat will be.310 or higher.

The likelihood of obtaining at least 31 hits in 100 at-bats when the likelihood of a hit occurring in each at-bat is.

You may calculate 300 as follows:

P(31 hits or more in 100 at-bats) = 1 - P(30 hits or fewer in 100 at-bats)

When the likelihood of getting a hit in each at-bat is, we can determine the likelihood of getting at least 31 hits in 100 at-bats using the normal approximation. the following 300:

P(31 hits or more in 100 at-bats) = 1 - P(30 hits or fewer in 100 at-bats)

substitute the values in the above equation

= 1 - P(z ≤ (30 - 100(.300)) / √(100(.300)(1 - .300)))

simplifying the equation, we get

= 1 - P(z ≤ -1.44)

= 1 - .0733

= .9267

As a result, there is a roughly.9267 chance that the player's average over his next 100 at-bats will be.310 or higher.

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Answer:

3/5 x 7

Step-by-step explanation:

The athlete swims 3/5 miles per day, and in 7 days, he swims the amount of 3/5 per the swimming session he does, so it will be 3/5x7.

In these options, 0ption D that is, Multicollinearity, is not an assumption of the regression model.

The regression model is a statistical technique used to model the relationship between a dependent variable and one or more independent variables. There are several assumptions associated with the regression model, which should be satisfied for accurate and reliable results.

Option A, Linearity, assumes that there is a linear relationship between the independent variables and the dependent variable. It implies that the relationship can be represented by a straight line.

Option B, Independence, assumes that the observations or data points used in the regression model are independent of each other. This means that the value of one observation does not depend on or influence the value of another observation.

Option C, Homoscedasticity, assumes that the variance of the errors or residuals in the regression model is constant across all levels of the independent variables. It implies that the spread or dispersion of the residuals is consistent.

Option D, Multicollinearity, is not an assumption of the regression model. Multicollinearity refers to a high correlation between independent variables in the regression model, which can cause issues in estimating the individual effects of the independent variables.

Therefore, the correct answer is D) Multicollinearity, as it is not an assumption of the regression model.

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