\(\sf\large\green{\underbrace{\red{Question*}}}:\)
Solve for p
\( \frac{p}{3 } > 2(p + 7)\)
​

Answer:

The regular costs 11 dollars each while the deluxe cost 23 each.

Step-by-step explanation:

You need to setup two equations.I used two variable for the prices of the types of pizzas because they are unknown.I used x for the cost of regular and y for the cost of deluxe.The equation I did are 10x+y=133 and 7x+9y=284.You need to solve one equation only.I solved the first one.

Answer:

The width is 26cm and the length is 47cm :)

Step-by-step explanation:

im doing this rn

Answer:

125x - 33x⁴

Pull out like factors :

125x - 27x⁴ = -x • (27x3 - 125)

Factoring: 27x³- 125

Theory : A difference of two perfect cubes, a³ - b³ can be factored into

(a-b) • (a² +ab +b²)

(a-b)•(a²+ab+b²) =

a³+a²b+ab²-ba²-b²a-b³ =

a³+(a2b-ba²)+(ab²-b²a)-b³ =

a³+0+0+b³ =

a³+b³

Check : 27 is the cube of 3

Check : 125 is the cube of 5

Check : x³ is the cube of x¹

Factorization is :

(3x - 5) • (9x² + 15x + 25)

\( \)

The final point after reflecting (-4, -7) twice across the x-axis is (-4, 7).To reflect a point across the x-axis, we change the sign of its y-coordinate while keeping the x-coordinate the same.

Given the initial point (-4, -7), let's perform the first reflection across the x-axis. By changing the sign of the y-coordinate, we get (-4, 7). Now, to perform the second reflection across the x-axis, we once again change the sign of the y-coordinate. In this case, the y-coordinate of the previously reflected point (-4, 7) is already positive, so changing its sign results in (-4, -7). Therefore, after reflecting the point (-4, -7) across the x-axis twice, the final point is (-4, 7). The reflection process can be visualized as flipping the point across the x-axis. Initially, the point (-4, -7) lies below the x-axis. The first reflection across the x-axis brings it to the upper side of the x-axis, resulting in (-4, 7). The second reflection flips it back down below the x-axis, yielding the final point (-4, -7).It's worth noting that reflecting a point across the x-axis twice essentially cancels out the reflections, resulting in the point returning to its original position. In this case, the original point (-4, -7) and the final point (-4, -7) have the same coordinates, indicating that the double reflection has brought the point back to its starting location.

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Answer:

I have one so far, 9.3x10^6 =9300000

a) The divergence of f = \(e^{xy\) i - cosy j + sin z²k is y \(e^{xy\) + sin y + 2z cos z², and the curl is 0.

b) The divergence of f = xi + yj - zk is 1, and the curl is 0.

a) To find the divergence and curl of the vector field f = \(e^{xy\) i - cosy j + sin z²k:

Divergence:

The divergence of a vector field f = P i + Q j + R k is given by the formula:

div(f) = ∇ · f = ∂P/∂x + ∂Q/∂y + ∂R/∂z

Given f = \(e^{xy\) i - cosy j + sin z²k, we can calculate the divergence as follows:

∂P/∂x = ∂/∂x(\(e^{xy\)) = y \(e^{xy\)

∂Q/∂y = ∂/∂y(-cosy) = sin y

∂R/∂z = ∂/∂z(sin z²) = 2z cos z²

Therefore, the divergence of f is:

div(f) = y \(e^{xy\) + sin y + 2z cos z²

Curl:

The curl of a vector field f = P i + Q j + R k is given by the formula:

curl(f) = ∇ × f = ( ∂R/∂y - ∂Q/∂z ) i + ( ∂P/∂z - ∂R/∂x ) j + ( ∂Q/∂x - ∂P/∂y ) k

Using the vector field f = \(e^{xy\) i - cosy j + sin z²k, we can calculate the curl as follows:

∂P/∂y = ∂/∂y(\(e^{xy\)) = x \(e^{xy\)

∂Q/∂z = ∂/∂z(-cosy) = 0

∂R/∂x = ∂/∂x(sin z²) = 0

∂R/∂y = ∂/∂y(sin z²) = 0

∂Q/∂x = ∂/∂x(-cosy) = 0

∂P/∂z = ∂/∂z(\(e^{xy\)) = 0

Therefore, the curl of f is:

curl(f) = (0 - 0) i + (0 - 0) j + (0 - 0) k

curl(f) = 0 i + 0 j + 0 k

curl(f) = 0

b) To find the divergence and curl of the vector field f = xi + yj - zk:

Divergence:

∂P/∂x = ∂/∂x(x) = 1

∂Q/∂y = ∂/∂y(y) = 1

∂R/∂z = ∂/∂z(-z) = -1

Therefore, the divergence of f function is:

div(f) = ∇ · f = 1 + 1 - 1 = 1

Curl:

∂P/∂y = ∂/∂y(x) = 0

∂Q/∂z = ∂/∂z(y) = 0

∂R/∂x = ∂/∂x(-z) = 0

∂R/∂y = ∂/∂y(-z) = 0

∂Q/∂x = ∂/∂x(y) = 0

∂P/∂z = ∂/∂z(x) = 0

Therefore, the curl of f is:

curl(f) = (0 - 0) i + (0 - 0) j + (0 - 0) k

curl(f) = 0 i + 0 j + 0 k

curl(f) = 0

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The meterstick must be moving at a velocity of approximately 0.836 times the speed of light (or about 251,547,246 m/s) for its length to be measured as 0.737 m.

According to this theory, the length of an object moving relative to an observer appears to be shorter than its rest length. The amount of length contraction depends on the relative velocity between the observer and the object, as well as the direction of motion.

The formula for length contraction is given by:

\(L' = L \times \sqrt{(1 - v^2/c^2)}\)

where L is the rest length of the object, L' is its length as measured by the observer, v is the relative velocity between the observer and the object, and c is the speed of light.

In this case, we are given that the measured length of the meterstick is 0.737 m. We can assume that the rest length of the meterstick is the standard length of a meterstick, which is 1.0 m. We want to find the velocity v at which this length contraction occurs.

So, we can rearrange the formula above to solve for v:

\(v = c \times \sqrt{(1 - (L'/L)^2)}\)

Plugging in the values given, we get:

\(v = c \times \sqrt{(1 - (0.737/1.0)^2)} \\= c \times \sqrt{(1 - 0.542^2)} \\= c \times \sqrt{v} \\= 0.836c\)

where c is the speed of light (299,792,458 m/s).

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Answer:

Step-by-step explanation:

90% of the sample means will be greater than 28.464 minutes for an oil and filter change on an automobile.

To find the value such that 90% of the sample means will be greater than it, we'll use the following terms: mean, standard deviation, sample size, and Z-score:

1. The mean (µ) of the population is 30 minutes.
2. The standard deviation (σ) of the population is 6 minutes.
3. The sample size (n) is 25 cars.
4. To find the standard error (SE) of the sample means, divide the standard deviation by the square root of the sample size: SE = σ / √n = 6 / √25 = 6 / 5 = 1.2 minutes.
5. For a 90% confidence interval, we want to find the Z-score corresponding to the 10th percentile (since 90% of the sample means will be greater than this value). Using a Z-table or a calculator, we find that the Z-score is approximately -1.28.
6. Multiply the Z-score by the standard error: -1.28 * 1.2 = -1.536 minutes.
7. Add this value to the mean: 30 + (-1.536) = 28.464 minutes.

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In the regression model without an intercept, yi = B1xi + Er for i=1,2,...,n, the total sum of squares (SST) need not be equal to the residual sum of squares (SSR) + explained sum of squares (SE) due to the absence of the intercept term.

SST represents the total variation in the dependent variable (yi), which is typically decomposed into explained variation (SE) and unexplained variation (SSR) in the presence of an intercept. However, when the model doesn't include an intercept, this decomposition does not hold true.

The reason is that without an intercept, the regression line is forced to go through the origin (0,0), which can result in a poor fit of the data. Consequently, the explained sum of squares (SE) may not accurately capture the variability explained by the model, and the residual sum of squares (SSR) might not account for the remaining unexplained variation.

Therefore, in a regression model without an intercept, the relationship SST = SSR + SE may not hold true, as the decomposition of total variability into explained and unexplained components is disrupted by the lack of an intercept term.

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The measure of arc BC is 6 in, which is equal to the radius of the circle.

The answer is 6 in.

The measure of an arc is equal to the measure of the central angle that intercepts it. In the diagram, the arc BC is intercepted by the central angle BOC. The measure of central angle BOC is 180 - 90 = 90 degrees. Therefore, the measure of arc BC is also 90 degrees.

The circumference of a circle is equal to 2 * pi * r. In the diagram, the radius of the circle is AB = 3 in. Therefore, the circumference of the circle is 2 * pi * 3 = 6 pi in.

The measure of arc BC is 90 degrees, which is 1/6 of the circumference of the circle. Therefore, the measure of BC is 6 pi / 6 = 6 in.

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Answer:  A

Step-by-step explanation:

When multiplying: Numbers multiply with numbers and for the x's, add the exponents

If there is no exponent, you can assume an imaginary 1 is the exponent

2x⁴ (3x³ − x² + 4x)

= 6x⁷ -2x⁶ + 8x⁵

Answer:

A. \(6x^{7} - 2x^{6} + 8x^{5}\)

Label the parts of the expression:

Outside the parentheses = \(2x^{4}\)

Inside parentheses = \(3x^{3} -x^{2} + 4x\)

You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses

\(2x^{4}\) × \(3x^{3}\)

\(2x^{4}\) × \(-x^{2}\)

\(2x^{4}\) × \(4x\)

First, multiply the whole numbers of each value before the variables

2 x 3 = 6

2 x -1 = -2

2 x 4 = 8

Now you have:

6\(x^{4}x^{3}\)

-2\(x^{4}x^{2}\)

8\(x^{4} x\)

When you multiply exponents together, you multiply the bases as normal and add the exponents together

\(6x^{4+3}\) = \(6x^{7}\)

\(-2x^{4+2}\) = \(-2x^{6}\)

\(8x^{4+1}\) = \(8x^{5}\)

Put the numbers given above into an expression:

\(6x^{7} -2x^{6} +8x^{5}\)

distribution

variable

like exponents

If a random sample of 20 gas stations was selected to estimate the gas prices. The type of error that could have occurred is a type I error, which is the rejection of a true null hypothesis. The probability of making a type I error is equal to the level of significance (α), which is 10% in this case. So, there is a 10% chance of making a type I error in this test.

To test if the true average gas price is under $3.50, we can use a one-tailed t-test with a null hypothesis of:

H0: μ >= $3.50

And an alternative hypothesis of:

Ha: μ < $3.50

where μ is the true population mean gas price.

Using a t-test with a sample size of 20, we can calculate the t-value as:

t = (x -bar - μ) / (s / sqrt(n))

where x-bar is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the given values, we get:

t = (3.40 - 3.50) / (0.22 / sqrt(20))

t = -2.03

Looking up the t-distribution table with degrees of freedom (df) = 19 and a 10% alpha level (α = 0.10), we find the critical t-value as -1.325.

Since our calculated t-value (-2.03) is less than the critical t-value (-1.325), we reject the null hypothesis in favor of the alternative hypothesis. Therefore, we can conclude that there is sufficient evidence to suggest that the true average gas price is under $3.50.

The type of error that could have occurred is a Type I error, which is rejecting a true null hypothesis. In this case, it means that we conclude that the true average gas price is under $3.50 when it's actually not. The probability of making a Type I error is equal to the alpha level, which is 10% in this case. So there's a 10% chance that we falsely reject the null hypothesis.

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Answer:

if i answered it would be 0

Step-by-step explanation:

To find a coterminal angle within [0, 2π], we can subtract 2π from θ until we get an angle within [0, 2π].θ - 2π = 17 - 2π ≈ 11.84955, So a coterminal angle of θ in [0, 2π] is approximately 11.84955.

a) Coterminal angle in [0, 2π] is the angle that terminates in the same place on the unit circle as the given angle. For this, we can add or subtract multiples of 2π to the given angle until we get an angle within the interval [0, 2π].In this case, the given angle is θ = 17.

b) The reference angle is the acute angle formed between the terminal side of the angle and the x-axis. To find the reference angle for θ = 17, we need to subtract 2π from θ until we get an angle in the interval [0, π/2).θ - 2π = 17 - 2π ≈ 11.84955Since 11.84955 is in the interval [0, π/2), the reference angle for θ = 17 is approximately 11.84955.

c) To find sin θ exactly, we need to know the reference angle for θ. We already found in part (b) that the reference angle is approximately 11.84955.Since sin θ is negative in the second quadrant,

we need to use the fact that sin(-x) = -sin(x).

Therefore, sin θ = -sin(π - θ) = -sin(π/2 - 11.84955) = -cos 11.84955 ≈ -0.989.

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The equation would be -x+10.2-\(\frac{1}{2}\)x+y

The equation contains:

-decimals

-variables

-negatives

-fractions

-like-terms

Answer:

The algebraic expression has one constant, 10.2, which is a number by itself. The variables, which are letters that stand for unknown values, are x and y. The coefficients, which are numbers that are multiplied to the variables, are

-1, -1/2, and 1. The terms that have an x are like terms.

Step-by-step explanation:

Answer:

-1 , -24

Step-by-step explanation:

x*2 + x +24x +24

x(x+1) 24(x+1)

(x+24) (x+1)

x=-24. x=-1

Answer:  (x+24)(x+1)

Step-by-step explanation:

Factor means to find 2 thing that multiply to the thing before.

x² + 25x + 24

In order to factor you need to find 2 numbers that multiply to the last term, +24 but adds to the middle term, +25.

24 and 1 multiply to +24 but also adds to +25

24 and 1 are you factor numbers that you will use to put into factored form.

(x+24)(x+1)

"The approximate value of D(4) is 24.6976." Please double-check your calculations and ensure that you correctly evaluated e^(-0.6) in your initial attempt. If you received a different answer, there may have been an error in the calculation.

To evaluate the expression D(4) = 45e^(-0.15(4)), we can follow the order of operations.

First, we simplify the exponent inside the parentheses:

-0.15(4) = -0.6

Next, we substitute this value back into the expression:

D(4) = 45e^(-0.6)

Using the properties of exponential functions, we can rewrite this as:

D(4) = 45 * e^(-0.6)

Now, we can calculate the value of e^(-0.6) using a calculator or mathematical software:

e^(-0.6) ≈ 0.5488 (rounded to four decimal places)

Finally, we substitute this value back into the expression:

D(4) ≈ 45 * 0.5488 ≈ 24.6976.

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When performing a statistical test, such as the Chi-Square test, the p-value is a crucial component in determining the significance of the data compared to the null hypothesis. The p-value represents the probability of observing the given data, or more extreme results, assuming the null hypothesis is true. In general, a p-value threshold of 0.05 is used to determine statistical significance.

If the calculated p-value is less than or equal to 0.05, it indicates that the observed data significantly differ from what is expected under the null hypothesis. This means that there is a less than 5% chance of obtaining the observed data if the null hypothesis were true. Consequently, researchers often reject the null hypothesis in favor of the alternative hypothesis when the p-value is less than or equal to 0.05.

However, it is essential to note that the choice of the significance level is subjective and may vary depending on the field or specific study. In some cases, a more stringent threshold, such as 0.01, might be required to minimize the chances of false positives, while in other situations, a more lenient threshold, such as 0.10, may be acceptable.

In summary, a p-value of 0.05 or less typically indicates that the data differ significantly from what is expected under the null hypothesis in a statistical test like the Chi-Square test. However, the chosen threshold for significance may vary depending on the specific context and research objectives.

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Answer:

Jason earns $12 +$50 =62$ in 1hour

Alyssa earns 22$ in a hour

now Jason have to work for 1 hour and Alyssa have to work for 62÷22 = 2.81 hour

to make same amount of money..

please brainleaist

Answer:

(-10,6)

Step-by-step explanation:

Domain only refers to x values so for this problem you would simply put (-10,6) since -10 is the lowest value and 6 is highest value.

Answer:

2(3x+6)=18

6x+12=18

6x+12-12+18-12

6x=6

6x/6=6/6

x=1

Step-by-step explanation:

Answer:

$0.27 per oz

I hope this helps :)

The given dynamic programming problem aims to maximize the objective function 2x + 3x + 4x, with the constraint that certain expressions involving x are integers. The optimal solution is (0, 2, 0), with a maximum objective function value of 6.



To formulate the problem as a dynamic programming problem, let's denote the stages as 1, 2, and 3. Each stage represents the choices we can make for the variable x. We need to maximize the objective function 2x + 3x + 4x subject to the constraint that 2x + 2, 3x + 54, etc., are integers.

We can define the state S as the current value of x. The transitions T(S, d) represent the possible values of x in the next stage, considering the amount of slack available in the constraint. The cost c(S, d) is the coefficient of x in the objective function.

Using the given table, we can calculate the optimal value of the objective function for each state at each stage. The optimal solution is (x)* = (0, 2, 0), and the maximum value of the objective function is 6.

To change the objective function, you can adjust the coefficients accordingly and recalculate the optimal solution using the same dynamic programming approach.

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A statistical analysis is internally valid if option B is correct, meaning that the statistical inferences about causal effects are valid for the population studied. Internal validity refers to the accuracy of conclusions drawn from a study, specifically focusing on causal relationships within the population being analyzed.

Statistical analysis is a method of examining data to identify patterns and trends, which can help researchers make informed decisions. Regression is a technique used to determine the relationship between two or more variables, where one variable (the dependent variable) is affected by one or more other variables (independent variables).

The population refers to the entire group of individuals or objects being studied. In order to have internal validity, the statistical analysis must accurately represent the population's characteristics and the causal relationships between variables.

R² (option A) is a measure of how well the regression model fits the data but doesn't necessarily imply internal validity. Option C, t-statistics, is related to hypothesis testing and helps determine if a relationship between variables is statistically significant. However, having all t-statistics greater than |1.96| doesn't guarantee internal validity.

Lastly, option D states that the population is small (less than 2,000) and can be observed. While having a smaller population might make it easier to gather data, this does not guarantee internal validity.

In summary, internal validity is achieved when the statistical inferences about causal effects are valid for the population studied (option B). It ensures that the conclusions drawn from a study are accurate and represent the true relationships within the population.

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Answer:

Z - score = 2.83

Step-by-step explanation:

Given the following :

Number of samples (N) = 60

Sample mean (x) = 41.9mg

Population mean (μ) = 40mg

Population standard deviation (sd) = 5.2

Using the relation :

Z = (x - μ) / (sd / √N)

Z = (41.9 - 40) / (5.2 / √60)

Z = 1.9 / (5.2 / 7.7459666)

Z = 1.9 / 0.6713171

Z = 2.8302570

Therefore, the z-score = 2.83

Answer:

y = 8x + 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 8 and c = 5

y = 8x + 5 ← equation of line

Answer:

The first person somehow

Step-by-step explanation: 10 divide by 2.7 is 3.7037037 and 10 divided by 2.4 is 4.16666667

To find the skewness of x, we need to first determine its probability density function (PDF) and its moments. Since x is a continuous uniform random variable with a minimum value of 1 and a maximum value of 1, its PDF is simply a constant function over the interval [1, 1]:

f(x) = 1/(1-1) = 1, for 1 ≤ x ≤ 1
     = 0, otherwise

The first moment of x is: μ₁ = E[X] = ∫₁¹ x*f(x) dx = ∫₁¹ x dx = 1/2

The second moment of x is: μ₂ = E[X²] = ∫₁¹ x²*f(x) dx = ∫₁¹ x² dx = 1/3

The third moment of x is: μ₃ = E[X³] = ∫₁¹ x³*f(x) dx = ∫₁¹ x³ dx = 1/4

Using these moments, we can calculate the skewness of x: γ₁ = (μ₃ - 3μ₁μ₂ + 2μ₁³) / σ³

where σ² = μ₂ - μ₁² is the variance of x. Plugging in the values we found earlier, we get: σ² = 1/3 - (1/2)² = 1/12
γ₁ = (1/4 - 3(1/2)(1/3) + 2(1/2)³) / (1/12)^(3/2) = 0

Therefore, the skewness of x is zero, which means that its distribution is perfectly symmetrical around its mean.

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Answer:

x = 71

Step-by-step explanation:

The chord- chord angle is half the sum of the arcs intercepted by the angle and its vertical angle, that is

x = \(\frac{1}{2}\) (92 + 50) = 0.5 × 142 = 71