Alex, Stephen and Bridget share some sweets in the ratio 4:1:1. Alex gets 36 sweets. How many sweets are there altogether?

Answer:

  yes

Step-by-step explanation:

You want a graph of P = 125 +50W.

The given equation is in slope-intercept form. The independent variable is W, and the dependent variable is P.

Usually, the independent variable is graphed on the horizontal axis, which you have done.

The dependent variable is graphed on the vertical axis, which you have done.

The axes are correctly labeled and graduated.

The "y-intercept" (P value) when the independent variable is zero is the constant in the equation, 125. You have correctly shown that on the graph.

The slope of the line is the coefficient of the independent variable (W) in the equation. You have correctly shown that P increases by 50 when W increases by 1.

Yes, you properly graphed the equation.

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The Product Rule of Logarithms states that the logarithm of a product is equal to the sum of the logarithms of the individual factors.

Therefore, we can expand the expression log5(3x + 6y) using the Product Rule of Logarithms as follows:

log5(3x + 6y) = log5(3(x + 2y))

= log5(3) + log5(x + 2y)

So the completely expanded expression equivalent to log5(3x + 6y) using the Product Rule of Logarithms is log5(3) + log5(x + 2y). The logarithm of 3 is a constant, so it can be written as a single term. The second logarithm cannot be simplified further because the sum of x and 2y is inside the logarithm function. It is important to use parentheses around the logarithm function when expanding logarithmic expressions to ensure that the order of operations is maintained.

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Answer:

1lb would be 6.75 because you need to divide 20.25 by 3 lb

Step-by-step explanation:

Answer:

5.73

Step-by-step explanation:

The difference is 5.73.

During the time Charlotte takes her eyes off the road for 0.35 s, she continues to travel at a speed of 53.1 mi/h. To find the distance she has traveled in feet, we can use the formula: Distance = Speed × Time.

Distance = 53.1 mi/h × (0.35 s) × (5280 ft/mi) / (3600 s/h) ≈ 70.038 ft

To calculate the distance traveled by Charlotte in feet, we need to convert the speed from miles per hour to feet per second and multiply it by the time she takes her eyes off the road.

First, we convert the speed from miles per hour to feet per second. Since 1 mile is equal to 5280 feet and 1 hour is equal to 3600 seconds, we can convert the speed as follows: 53.1 mi/h × (5280 ft/mi) / (3600 s/h) ≈ 77.8 ft/s.

Next, we multiply the speed (77.8 ft/s) by the time Charlotte takes her eyes off the road, which is 0.35 seconds. By multiplying these values, we obtain the distance traveled in feet during that time.

Therefore, Charlotte has traveled approximately 70.038 feet while looking down at her phone for 0.35 seconds. It is important to note that distracted driving can be dangerous, and it is crucial to prioritize road safety by avoiding distractions and keeping one's attention on the road.

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Answer:

1/3 * \(4\pi\) * h = 207, h = 155.25\(\pi\)

Step-by-step explanation:

Since we know the area of the base is \(4\pi\), that means the volume of the cone is:

1/3 * \(4\pi\) * h

If we substitue, we get:

1/3 * \(4\pi\) * h = 207

(This is the answer! If you want to solve, go below)

Now, we just solve

\(4\pi\\\) * h = 621

h = 621/\(4\pi\\\)

h = 155.25\(\pi\)

Answer:

The speed of sound is 2.23 times of the speed of race car

Step-by-step explanation:

Given that,

The speed of a race car = \(3.4\times 10^2\ mi/h\)

The speed of sound = \(7.6\times 10^2\ mi/h\)

Dividing the speed of sound to the speed of a race car. So,\(\dfrac{\text{speed of sound}}{\text{speed of race car}}=\dfrac{7.6\times 10^2}{3.4\times 10^2}\\\\\dfrac{\text{speed of sound}}{\text{speed of race car}}=2.23\)

So, the speed of sound is 2.23 times of the speed of race car.

Answer:

36 divided by 9 = 4 Skittles per Taki

3 x 4 = 12 Skittles

Step-by-step explanation:

I hope this helps! Have a nice day!

Answer:

It's quite simple, let me explain..

Step-by-step explanation:

The median is the middle of a data set, so you would need to find the exact middle of your data set.

If your data set is odd, and has an odd amount of numbers, just get the number exactly in the middle, and that would be your median. But when your data set has an even amount of numbers, it is a bit tricky.

Here's an example:

85, 78, 96, 83, 77

As you can see, this set has an odd amount of numbers, 5 numbers to be exact. The median would be 96 because it is exactly in the middle.

An example of a data set with even numbers would be this:

1, 2, 3, 4

What you would do is add the two numbers in the middle, and divide by two.

In this case, 2 and three are in the middle, so you would add 2 and 3, which is 5. Then you would divide 5 by two which is 2.5

2.5 Would be your median.

Hopefully this made sense, please ask questions if you have any.

Answer:

(9^3)^6

Step-by-step explanation:

This is an equivilant expression. Hope this helps!

Using stem-and-leaf plot, Option (d) choices include 13, 14, 16, 21, 22, 28, 29, 30, 32, 34, 34, and 45.

To display numerical data, a stem and leaf plot separates each data point into a "leaf" (typically the last digit) and a "stem" (the leading digit or digits).

Stem and leaf plot in this query

1 ∣ 3 4 6

2 ∣ 1 2 8 9

3 ∣ 0 2 4 4

4 ∣ 5

Key: 1 | 3 equals 13.

Slice the leaf and stem -

1 | 3, 1 | 4, 1 | 6, 2 | 1, 2 | 2, 2 | 8, 2 | 9, 3 | 0, 3 | 2, 3 | 4, 3 | 4, 4 | 5

You'll see the selection every option that fits the data (d)

Consequently, the response will be 13, 14, and 16,  21, 22, 28, 29, 30, 32, 34, 34, 45

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The corresponding differential element, rewrite the integral in terms of the new variable, integrate with respect to the new variable, replace the new variable with the original variable, and simplify the expression to find the solution.

To perform u-substitution with indefinite integrals, follow these steps:

Identify a suitable substitution: Look for a part of the integrand that resembles the derivative of a function. Choose a variable u to substitute for that part.

Calculate du: Take the derivative of u with respect to the original variable. This will help us express du in terms of the original variable.

Rewrite the integral: Substitute the chosen variable and du in the original integral, replacing the part to be substituted with u and the corresponding differential element du.

Integrate with respect to u: Treat the integral as a new integral with respect to u. Evaluate the integral using the rules of integration.

Replace u with the original variable: Rewrite the result of the integration in terms of the original variable.

Simplify and solve: If necessary, simplify the expression further or perform additional algebraic manipulations to obtain the final result.

Let's illustrate these steps with an example:

Consider the integral ∫(2x + 3)² dx.

Identify a suitable substitution: Let u = 2x + 3.

Calculate du: Take the derivative of u with respect to x: du/dx = 2. Rearrange the equation to solve for du: du = 2 dx.

Rewrite the integral: In terms of u and du, the integral becomes ∫u² (du/2).

Integrate with respect to u: Treat the integral as a new integral with respect to u: (1/2) ∫u² du = (1/2) * (u³/3) + C, where C is the constant of integration.

Replace u with the original variable: Substitute back u = 2x + 3 in the result: (1/2) * ((2x + 3)³/3) + C.

Simplify and solve: Further simplify the expression if necessary to obtain the final result.

In summary, to perform u-substitution with indefinite integrals, identify a suitable substitution, calculate the corresponding differential element, rewrite the integral in terms of the new variable, integrate with respect to the new variable, replace the new variable with the original variable, and simplify the expression to find the solution.

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Answer:

A

Step-by-step explanation:

The triangles are the same. Congruent is when all three sides are equal to each other on both triangles

Answer:

plot the points

(-4, 2.5) (-3, 3) (-2, 1.5) (-1, 2) (0, 1)

(1, 2) (2, 3.5) (3, 0.5) (4, 2.5)

Step-by-step explanation:

does that help any???

Answer: $574

Step-by-step explanation:

First we need to calculate the price of the snowboard before the addition of the tax. This will be represented by x. Therefore,

6% of x = $32.50

0.06 × x = $32.50

0.06x = $32.50

x = $32.50 / 0.06

x = $541.67

Therefore, the total cost including the sales tax will be:

= $541.67 + $32.50

= $574.17

= $574

Answer:

$345 : whichever is closest

Step-by-step explanation:

Pants were $20 each and she bought 9 of them so multiply:

9x20=180

She paid $180 for 9 pants.

Shirts cost $15 each and she bought 11 of them so Mulitply:

15x11=165

She paid $165 for 11 shirts

Add both totals from pants and shirts

165+180=$345

Answer: 350

Step-by-step explanation: I dont really now how but 345 is close to 350 and my learning app says so.I'M really bad at math but if get this questoin an Modymax than the awsnser is 350.

Answer:

If my answer is correct for you please mark me brainliest answer if you want please please thanks thanks thanks thanks thanks thanks

Answer:

y = - 6

Step-by-step explanation:

Given:

x = - 2

Equation:

y = 5x + 4

Step 1: Substitute x

y = 5 ( - 2 ) + 4

Step 2: Simplify

y = - 10 + 4

Answer:

y =  - 6

Whave established that the series l~=l an - z converges uniformly for Re(z) ≤ c

What is uniformly?

The keyword "uniformly" refers to the concept of uniform convergence. In the context of the given question, it is stated that the series l~=l an - z converges uniformly for Re(z) ≤ c. Uniform convergence means that the convergence of the series is independent of the value of z within a certain range (Re(z) ≤ c in this case).

To show that the series l~=l an - z converges uniformly for Re(z) ≤ c, where an is a bounded sequence of complex numbers and we choose the principal branch of n - z, we need to demonstrate that for any ε > 0, there exists an N such that for all n > N and for all z with Re(z) ≤ c, the inequality |l~=l an - z| < ε holds.

Given that an is a bounded sequence, there exists an M > 0 such that |an| ≤ M for all n.

Let's consider the series l~=l an - z. We can write it as:

l~=l an - l z.

Now, since |an| ≤ M for all n, we have:

|an - z| ≤ |an| + |z| ≤ M + c.

By choosing N such that M + c < ε, we can ensure that for all n > N and for all z with Re(z) ≤ c, the inequality |an - z| < ε holds.

Now, using the triangle inequality, we have:

|l~=l an - z| ≤ |an - z|.

Since we have shown that |an - z| < ε for n > N and Re(z) ≤ c, it follows that |l~=l an - z| < ε for n > N and Re(z) ≤ c.

Therefore, we have established that the series l~=l an - z converges uniformly for Re(z) ≤ c.

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SOLUTION:

Case: Quadratic Application Word Problem

Given:

Required:

a. How long did it take for Jason to reach his maximum height?

b. What was the highest point that Jason reached?

c. What is Jason’s initial height?

Method:

Step 1: How long did it take for Jason to reach his maximum height?

To calculate this, we find the vertex

From here, the vertex is at (1/2, 484).

Hence it takes 1/2 a second to reach the maximum height

Step 2: What was the highest point that Jason reached?

Also, from the vertex, we get the highest height reached

The maximum height reached was 484 feet

Step 3: What is Jason’s initial height?

The initial height is gotten at the start of the motion, i.e. h(0) = ?

Hence the initial height was 480 feet

Final answer:

A) Time = 1/2 second

B) Maximum Height, H= 484 feet

C) Initial Height, H= 480 feet

The reliability of the given system is 0.4033.

To calculate the reliability of a system, we need to multiply the reliability values of all the components in the system. In this case, we have a system composed of three components with the following reliability values:

Component 1: 0.90

Component 2: 0.90 0.90 0.85

Component 3: 0.85 0.85 0.92

To find the overall system reliability, we multiply these values together:

System reliability = Component 1 reliability x Component 2 reliability x Component 3 reliability

System reliability = 0.90 x (0.90 x 0.90 x 0.85) x (0.85 x 0.85 *x 0.92)

System reliability ≈ 0.90 x 0.6831 x 0.6528 ≈ 0.4033

Therefore, the reliability of the given system is 0.4033.

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Linear equations involve equalities (i.e., "=") and are used to represent lines in a coordinate plane. Linear inequalities, on the other hand, involve inequalities (i.e., "<", ">", "<=", ">=") and are used to represent regions or areas of a coordinate plane that satisfy certain conditions.

A linear equation can be expressed in the form "y = mx + b," where "m" represents the slope of the line and "b" represents the y-intercept. Given the values of "m" and "b," you can calculate the y-coordinate for any given x-coordinate, and vice versa. The graph of a linear equation is a straight line.

A linear inequality is expressed in the form "y < mx + b," "y > mx + b," "y <= mx + b," or "y >= mx + b." Instead of representing a single line, a linear inequality represents a shaded region on the coordinate plane that satisfies the given condition. To graph a linear inequality, you can choose a test point not on the line and check whether it satisfies the inequality. If it does, shade the region containing the test point; otherwise, shade the other region.

In summary, the main difference between linear equations and linear inequalities is the use of equalities versus inequalities. Linear equations represent lines, while linear inequalities represent shaded regions on the coordinate plane. Equations deal with exact solutions, whereas inequalities deal with a range of possible solutions. Understanding the distinctions between these concepts is important in various areas of mathematics, such as algebra and geometry.

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Answer: 72 beads

Step-by-step explanation:

From the question, we have the information that Johnathan picked colored beads from a jar 50 times and replaced the bead each time. Jonathan picked a red bead 12 times, yellow bead 14 times, and a blue bead 24 times.

Out of 50 picks, the following beads were picked:

Red = 12

Yellow = 14

Blue = 24

Total = 50

Fraction of blue bead = 24/50 × 100

= 48%

The blue beads that Johnathan will pick out of 150 beads will be:

= 48% of 150

= 48/100 × 150

= 0.48 × 150

= 72 blue beads

Jonathan will pick 72 blue beads out of 150 beads.

Answer:

72 beads

:):):):):):):):)

Answer:

Step-by-step explanation:

The point (-5, 2, -1) in spherical coordinates is (r, θ, φ) = (\(\sqrt{30}\), 2.3038, 5.8628) or approximately (5.5, 132.2°, 335.7°).

To convert the point (-5, 2, -1) from Cartesian coordinates to spherical coordinates, we need to find its radial distance (r), polar angle (θ), and azimuthal angle (φ).

The radial distance r is given by:

r = \(\sqrt{x^2 + y^2 + z^2}\)

Substituting the given values, we get:

r = \(\sqrt{((-5)^2 + 2^2 + (-1)^2)}\) = \(\sqrt{30}\)

The polar angle θ is the angle between the positive z-axis and the line connecting the point to the origin. It can be found using:

θ = \(cos^(-1)(z / r)\)

Substituting the given values, we get:

θ = \(cos^(-1)(-1 /\sqrt{30} ))\) = 2.3038 radians (approx.)

The azimuthal angle φ is the angle between the positive x-axis and the projection of the line connecting the point to the origin onto the xy-plane. It can be found using:

φ =\(tan^(-1)(y / x)\)

Substituting the given values, we get:

φ = \(tan^(-1)(2 / (-5))\) = -0.3805 radians (approx.)

Note that the result is negative because the point is in the third quadrant of the Cartesian coordinate system. To get a positive value for φ, we can add 2π radians to the result:

φ = -0.3805 + 2π = 5.8628 radians (approx.)

Therefore, the point (-5, 2, -1) in spherical coordinates is (r, θ, φ) = (sqrt(30), 2.3038, 5.8628) or approximately (5.5, 132.2°, 335.7°).

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The value of x in the tangent intersection is 6.

The measure of the angle between the two tangents is also half the difference between the major and minor arcs between the two points of contact with the tangents.

Therefore, using the tangent intersection theorem, the value of x can be found as follows:

9x + 1 = 1 / 2(235 - (360 - 235))

9x + 1 = 1 / 2 (235 - 125)

9x + 1 = 1 / 2 (110)

9x + 1 = 55

Therefore,

9x = 55 - 1

9x = 54

divide both sides of the equation by 9

x = 54 / 9

x = 6

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A 99% confidence interval for the true proportion of teens aged 13-17 who have their own desktop or laptop computer can be calculated using the information provided in the nationwide random survey of 1,500 teens. In the survey, approximately 65% (or 0.65) of the respondents indicated that they have their own computer.

To calculate the confidence interval, we'll use the formula:

CI = p-hat ± Z * √(p-hat * (1 - p-hat) / n)

where:
- CI represents the confidence interval
- p-hat is the sample proportion (0.65)
- Z is the Z-score corresponding to the desired confidence level (2.576 for a 99% confidence interval)
- n is the sample size (1,500)

Now, let's plug in the values:

CI = 0.65 ± 2.576 * √(0.65 * 0.35 / 1,500)

CI = 0.65 ± 2.576 * 0.0128

CI = 0.65 ± 0.0330

So, the 99% confidence interval is (0.617, 0.683).

This means that, based on the survey results, we can be 99% confident that the true proportion of teens aged 13-17 who have their own desktop or laptop computer is between 61.7% and 68.3%.

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