- Olu has 2x oranges and Umar has 4 oranges less than Olu. How many oranges do they have altogether?​

Answer:

A movie costs $4.25 and a video game $5.5.

Step-by-step explanation:

Step 1: Form the equations.

Let m be the price of a movie and v the price of the video game.

First equation: One month Jessica rented 4 movies and 8 video games for a total of $61.

\(4m + 8v = 61\)

Second equation: The next month she rented 2 movies and 3 video games for a total of $25.

\(2m + 3v = 25\)

Step 2: Solve the system of equations.

\(\text{(1.) } 4m + 8v = 61\\\text{(2.) } 2m + 3v = 25\)

I'm going to solve them by elimination. I'll multiply the second equation with two so I get 4m.

\(\text{(1.) } 4m + 8v = 61\\\text{(2.) } 4m + 6v = 50\)

Now I'm going to subtract the second equation from the first.

\((4m + 8v) - (4m + 6v) = 61 - 50\)

And solve.

\(8v- 6v = 61 - 50\\2v = 11\\v = \frac{11}{2}\\v = \$5.5\)

Now let's insert v back in second equation to get m (nicer numbers, you can insert in first too if you want).

\(4m + 8v = 61\\4m + 8(5.5) = 61\\4m + 44 = 61\\4m = 61 - 44\\4m = 17\\m = \frac{17}{4}\\m = \$4.25\)

Answer: B

Step-by-step explanation:

if I'm wrong sry lol

Answer:

D

Step-by-step explanation:

- 117° is positioned in the 3rd quadrant where sine < 0

The related acute angle is 180° - 117° = 63°

Then

sin(- 117)°

= - sin63° → D

Answer:

In a pair of similar triangles, the corresponding sides are proportional. Corresponding sides touch the same two angle pairs. When the sides are corresponding it means to go from one triangle to another you can multiply each side by the same number

Answer:

It would be to ask all the students in the grade.

Step-by-step explanation:

Answer:

it D answer D and it will be correct I just did this test guys well if it isnt D then its all students in each grade I just did this test lol

Step-by-step explanation:

The value of x is after solving the logarithm equation logx⁽⁵¹²⁾ = 3 is 8.

A logarithmic equation is an equation that involves the logarithm of an expression containing a variable.

To solve the logarithm equation, we follow the steps below.

Given:

Step 1:

Therefore,

Step 2:

Convert 512 to index form. (i.e 8³)

Comparing both side of equation 1,

Hence, the value of x is 8.

Learn more about logarithm here: https://brainly.com/question/25993029

#SPJ1

Answer:

C should be the correct answer

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

Answer:

the last picture answer is

[alternate exterior angle ]

the third picture answer is

[alternate interior angle]

The probability of getting a diamond or a king from a standard 52-card deck is 4/13.

In mathematics, probability is a measure of the likelihood that an event will occur. It is a way to quantify the chances of different outcomes or events in a random experiment or process. Probability is typically expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event

In a standard deck of 52 cards, there are 13 diamonds and 4 kings. However, the king of diamonds is also a diamond, so we must subtract one from the total count to avoid double-counting.

So there are 13 + 4 - 1 = 16 cards that are either diamonds or kings.

The probability of picking a diamond or a king is therefore 16/52.

Simplifying the fraction, we get:

16/52 = 4/13

Learn more about probability here

brainly.com/question/11234923

#SPJ4

The standardized distribution known as the T distribution is a member of the one-parameter family. The degrees of freedom are the only input for the t distribution.

A measure of the distribution of a set of data points is called population variance. It measures the mean squared departure from the mean, specifically. As a result, the variance will be minimal if all of the data points are very near to the mean. The variation will be high if the data points are dispersed throughout a wide range.

The standardized distribution known as the T distribution is a member of the one-parameter family. The degrees of freedom are the only input for the t distribution. Because sample size is used to assess this degree of freedom, degrees of freedom are dependent on sample size.

The t distribution tends to follow a normal distribution as sample size rises. The degree of freedom is ultimately determined by the sample size, so as the degree of freedom rises, the t distribution tends to be a normal distribution.

To know more about population variances visit:
https://brainly.com/question/13708253

#SPJ4

The sets A and B, defined as A = {x ∈ Z | x = at + bs for some t, s ∈ Z} and B = {x ∈ Z | x = ct for some t ∈ Z}, are equal. This is because every element in A can be expressed as an element in B and vice versa, based on the properties of the greatest common divisor.

To prove that the sets A = B, where A = {x ∈ Z | x = at + bs for some t, s ∈ Z} and B = {x ∈ Z | x = ct for some t ∈ Z}, we need to show that every element in A is also in B, and vice versa.

First, let's show that every element in A is in B:

Let x be an element in A. This means there exist integers t and s such that x = at + bs.

Since c = gcd(a, b), we can express a and b as a = c * a' and b = c * b', where a' and b' are integers.

Substituting these expressions into x, we have:

x = (c * a')t + (c * b')s

x = c(a't + b's)

Since a't + b's is an integer (as it is the sum of two integers), we can let t' = a't + b's, where t' is also an integer.

Therefore, x = ct', where t' = a't + b's is an integer.

This shows that every element in A is in B.

Next, let's show that every element in B is in A:

Let x be an element in B. This means there exists an integer t such that x = ct.

Since c = gcd(a, b), we know that c divides both a and b. Therefore, we can express a and b as a = cx and b = cy, where x and y are integers.

Substituting these expressions into x, we have:

x = c * t

x = c * (xt)

Since xt is an integer (as it is the product of two integers), we can let s = xt, where s is also an integer.

Therefore, x = at + bs, where t = xt and s = y.

This shows that every element in B is in A.

Since we have shown that every element in A is in B and every element in B is in A, we conclude that A = B.

Hence, the sets A and B are equal, as desired.

To know more about greatest common divisor:

https://brainly.com/question/13257989

#SPJ4

The volume of the solid bounded below by the xy-plane, on the sides by ρ = 16, and above by φ = π/9, is approximately 2977.076 cubic units.

Here, we have,

To find the volume of the solid bounded below by the xy-plane, on the sides by ρ = 16, and above by φ = π/9,

we need to integrate the volume element ρ²sin(φ) dρ dφ dθ over the given region in spherical coordinates.

The limits of integration for the spherical coordinates are as follows:

ρ: from 0 to 16

φ: from 0 to π/9

θ: from 0 to 2π (for a full revolution around the z-axis)

The volume element in spherical coordinates is given by ρ² sin(φ) dρ dφ dθ.

Therefore, the volume V is calculated as follows:

V = ∫∫∫ ρ² sin(φ) dρ dφ dθ

V = ∫[0 to 2π] ∫[0 to π/9] ∫[0 to 16] ρ² sin(φ) dρ dφ dθ

Integrating with respect to ρ first:

V = ∫[0 to 2π] ∫[0 to π/9] (1/3) ρ³ sin(φ) |[0 to 16] dφ dθ

V = (1/3) ∫[0 to 2π] ∫[0 to π/9] (16³ sin(φ) - 0) dφ dθ

V = (1/3) ∫[0 to 2π] (16³) ∫[0 to π/9] sin(φ) dφ dθ

V = (1/3) (16³) ∫[0 to 2π] [-cos(φ)] |[0 to π/9] dθ

V = (1/3) (16³) ∫[0 to 2π] (-cos(π/9) + 1) dθ

V = (1/3) (16³) [(-cos(π/9) + 1)θ] |[0 to 2π]

V = (1/3) (16³) [(-cos(π/9) + 1)(2π - 0)]

V = (1/3) (16³) [(2π - 0)(1 - cos(π/9))]

V = (1/3) (16³) (2π - 0)(1 - cos(π/9))

V = (1/3) (16³) (2π)(1 - cos(π/9))

Now, we can calculate this value numerically:

V ≈ 2977.076 cubic units

Therefore, the volume of the solid bounded below by the xy-plane, on the sides by ρ = 16, and above by φ = π/9, is approximately 2977.076 cubic units.

To learn more on integration click:

brainly.com/question/26568631

#SPJ4

The general solution of the differential equation is: y = c1 e^(3t) cos(t) + c2 e^(3t) sin(t), where c1 and c2 are arbitrary constants determined by the initial or boundary conditions.

The given differential equation is a second-order homogeneous linear differential equation with constant coefficients. Its characteristic equation is obtained by assuming a solution of the form y = e^(rt), where r is a constant. Substituting this into the differential equation, we get:

r^2 e^(rt) - 6r e^(rt) + 10 e^(rt) = 0

Dividing both sides by e^(rt) (which is non-zero), we get:

r^2 - 6r + 10 = 0

Solving for r using the quadratic formula, we get:

r = (6 ± sqrt(6^2 - 4(1)(10))) / 2

r = 3 ± i

Therefore, the general solution of the differential equation is:

y = c1 e^(3t) cos(t) + c2 e^(3t) sin(t)

where c1 and c2 are arbitrary constants determined by the initial or boundary conditions.

This solution consists of a linear combination of two functions: the exponential function e^(3t) and the periodic function cos(t) or sin(t), which oscillates between -1 and 1. The exponential function represents the growth or decay of the system, while the periodic function represents the oscillations or vibrations of the system. The constants c1 and c2 determine the amplitude and phase of the oscillations, respectively. The behavior of the system depends on the signs and magnitudes of the real and imaginary parts of the roots, which determine whether the solutions are overdamped, critically damped, or underdamped.

Learn more about quadratic at: brainly.com/question/22364785

#SPJ11

The most accurate statement about the p-value for this test is: 0.05 < p-value < 0.10.

In a hypothesis test, the null hypothesis can be rejected at the .10 level but cannot be rejected at the .05 level. This means that the p-value for the test falls between these two levels.

A p-value is a measure of the strength of evidence against the null hypothesis. It represents the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value, assuming that the null hypothesis is true.

In this case, the fact that the null hypothesis can be rejected at the .10 level means that the p-value is less than .10. However since the null hypothesis cannot be rejected at the .05 level, it implies that the p-value is greater than .05.

This indicates that the evidence against the null hypothesis is not strong enough to reject it at the .05 level, but it is strong enough to reject it at the .10 level. The p-value falls between these two values, providing a range of uncertainty in the results of the hypothesis test.

In summary, the p-value in this scenario is greater than .05 but less than .10, indicating moderate evidence against the null hypothesis.

Learn more about  p-value

https://brainly.com/question/33325466

#SPJ11

In a hypothesis test, the null hypothesis can be rejected at the 0.10 level but cannot be rejected at the 0.05 level. This means that the p-value obtained in the test falls between these two levels.

The p-value is a measure of the strength of evidence against the null hypothesis. It represents the probability of observing the data or more extreme data, assuming that the null hypothesis is true.

When the p-value is less than the chosen significance level (alpha), typically 0.05, it indicates that the data provides strong evidence against the null hypothesis. In this case, we reject the null hypothesis in favor of the alternative hypothesis.

However, if the p-value is greater than the significance level, such as 0.10, it means that the data does not provide enough evidence to reject the null hypothesis. We fail to reject the null hypothesis and do not have sufficient evidence to support the alternative hypothesis.

Therefore, for this given hypothesis test, since the null hypothesis can be rejected at the 0.10 level but not at the 0.05 level, the most accurate statement about the p-value is:

0.05 < p-value < 0.10

This means that the p-value falls between 0.05 and 0.10, indicating moderate evidence against the null hypothesis, but not strong enough to reject it at the 0.05 level.

Learn more about null hypothesis

https://brainly.com/question/30821298

#SPJ11

x = 2 to x = 5 is 4.

To find the average rate of change of a function, you need to subtract the initial value from the final value and divide it by the change in the input variable. Here's how to use a calculator to find the average rate of change of a function:Step 1: Input the initial value of the input variable into the calculator.Step 2: Input the final value of the input variable into the calculator.Step 3: Subtract the initial value from the final value.Step 4: Divide the difference by the change in the input variable. Example:Find the average rate of change of the function f(x) = 3x - 1 from x = 2 to x = 5.Step 1: Input 2 into the calculator.Step 2: Input 5 into the calculator.Step 3: Subtract 3(2) - 1 from 3(5) - 1. The result is 14.Step 4: Divide 14 by 5 - 2. The result is 4.Therefore, the average rate of change of f(x) from x = 2 to x = 5 is 4.

Learn more about function

brainly.com/question/21145944

#SPJ4

hi

1/3 =2 /6

so 1/6 +2/6 = 3/6

as 3/6 is half if his income, then he remains the other half

What are you trying to say brother

we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

Learn more about Integrate here : brainly.com/question/31744185

#SPJ11

Answer:

It will have traveled 375 miles

Step-by-step explanation:

Answer:

75%

Step-by-step explanation:

To perform a translation of moving the equation x² + y² = 121 up 3 units, we modify the equation by adding 3 to the y-coordinate. The resulting equation is x² + (y + 3)² = 121.

To perform a translation of moving the equation x² + y² = 121 up 3 units, we need to modify the equation to reflect the new position. Since the translation is upward, we add 3 to the y-coordinate in the equation.

By adding 3 to the y-coordinate, the equation becomes x² + (y + 3)² = 121. This new equation represents the original equation shifted upward by 3 units.

The equation x² + (y + 3)² = 121 describes a circle centered at the origin with a radius of 11 units. The translation shifts this circle upward by 3 units, preserving its shape and size but changing its position in the coordinate plane.

Learn more about translation shifts here:

brainly.com/question/29163800

#SPJ11

Answer:

i wrote how to below!

Step-by-step explanation:

okay since the y intercept is 2, put a dot on the point (0, 2)

now for the next one just substitute an easy value like 1 to the equation

y = 3/4(4) + 2

the 4 will cancel out the denominator then...

y = 3 + 2

y = 5

now put a point on (4, 5)

Answer:

answer in explanation

Step-by-step explanation:

(0,2)

(1,2.75)

(2,3.5)

(3,4.25)

(4,5)

Answer: 5.474 m

Step-by-step explanation:

first jump = 4.25

best jump = first jump * 1.12

winning jump = best jump *1.15

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

Explanation:

Ignore the sides that are 'a' units long.

We'll compare the sides that are 26 units and 27 units long. We see the 27 unit side is larger, which makes the 93 degree angle larger than the 3x-9 degree angle.

Symbolically, we would say

3x-9 < 93

At the same time, the 3x-9 is also larger than 0

So

3x-9 > 0 or 0 < 3x-9

Put together, we can form this compound inequality

0 < 3x-9 < 93

-------------------

Let's isolate x like so

0 < 3x-9 < 93

0+9 < 3x-9+9 < 93+9 .... add 9 to all sides

9 < 3x < 102

9/3 < 3x/3 < 102/3 .... divide all sides by 3

3 < x < 34

x is any number between 3 and 34, but cannot equal either endpoint

For example, x = 10 is valid since 3 < 10 < 34 is true. But x = 50 is not a solution since 3 < 50 < 34 is false. We can't have x = 3 and we also can't have x = 34 either, but we can have anything in between those endpoints.

Answer:

(a) The probability that a contestant allowed to stay in the first episode is 0.5

(b) The probability that a contestant will be allowed to stay during both is 0.25

Step-by-step explanation:

The given parameters are;

The probability that a contestant who has been bribing the judges will be allowed to stay = 1

The probability that a contestant who has mot been bribing the judges will be allowed to stay = 1/3

The proportion of the contestant that has been bribing the judges = 1/4

The contestant who bribe the judges in the first round = The contestants who bribe the judges in the second round

(a) Let the total number of contestants = x

Therefore;

The number of contestants in the second round = x/4 + 1/3×(x - x/4) = x/2

Which gives that, half of the contestants make it to the second round

The probability that a contestant allowed to stay in the first episode, Pₐ₁, is given as follows;

Probability = (The number of required outcome)/(The number of possible outcome)

∴ Pₐ₁ = (x/4)/(x/2) = 2/4 = 1/2 = 0.5

The probability that a contestant allowed to stay in the first episode = 0.5

(b) The probability that a contestant will be allowed to stay during both episode, Pₐ₁₂ is given as follows;

The number of contestant that will be allowed to stay after each episode = 1/2×(The number contestant in the previous episode)

Therefore;

The number of contestant that will be allowed to stay after the first episode = 1/2 × x = x/2

The number of contestant that will be allowed to stay after the second episode = 1/2 × x/2 = x/4

Therefore, the number of contestant that will be allowed to stay after both episode = x/4

Pₐ₁₂ = (The number of contestant that will be allowed to stay after both episode)/(The total number of contestants)

∴ Pₐ₁₂ = (x/4)/x  = 1/4 = 0.25

The probability that a contestant will be allowed to stay during both = 0.25.

one real eigenvalue. find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace.

What is eigenvalue?

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that, when the linear transformation is applied to it, changes at most by a scalar factor. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by lambda.

a) -4

b) 1

c) 1

Step-by-step explanation:

a) The matrix A is given by:

\(A=\left[\begin{array}{ccc}-3 & 0 & 1 \\2 & -4 & 2 \\-3 & -2 & 1\end{array}\right]\\\)

where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:

\(A-\lambda I=\left[\begin{array}{ccc}-3-\lambda & 0 & 1 \\2 & -4-\lambda & 2 \\-3 & -2 & 1-\lambda\end{array}\right]\)

and by taking the determinant:\(\begin{aligned}& {[(-3-\lambda)(-4-\lambda)(1-\lambda)+(0)(2)(-3)+(2)(-2)(1)]-[(1)(-4-\lambda)(-3)+(0)(2)(1-} \\& \lambda)+(2)(-2)(-3-\lambda)]=0 \\& -\lambda^3-6 \lambda^2-12 \lambda-16=0\end{aligned}\)

and the roots of this polynomial is:

\(\begin{aligned}& \lambda_1=-4 \\& \lambda_2=-1+i \sqrt{3} \\& \lambda_3=-1-i \sqrt{3}\end{aligned}\)

hence, the real eigenvalue of the matrix A is -4.

b) The multiplicity of the eigenvalue is 1.

c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)

To learn more about eigenvalue visit

https://brainly.com/question/29579848

#SPJ4

Complete Quetion

The matrix A= (−3 0 1, 2 −4 2, −3 −2 1) has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace. The eigen value = has multiplicity = and the dimension of the corresponding eigenspace is:_______.

The value of cos (x + pi) is -✓3/2, based on the stated information and known trigonometric values.

As per the known fact, the value of x wil be 30° as it is the specific value whose cosine or cos is ✓3/2. Now, we also know that π represents 180°. Also, the formula for cos (a + b) is cos A cos B - sin A sin B.

So, cos (x + pi) will be -

cos x cos pi - sin x sin pi

Keeping the values and solving -

cos (x + pi) = cos 30 cos 180 - sin 30 sin 180

cos (x + pi) = (✓3/2 × -1) - (1/2 × 0)

cos (x + pi) = -✓3/2

Hence, the value of cos (x + pi) is -✓3/2.

Learn more about cosine -

https://brainly.com/question/24305408

#SPJ4

Answer:

Step-by-step explanation:

the top one... which is I am assuming asking for the diameter?

Formula = d=2r  

so 2x4 which is 8

But if you were wanting number 6

the formula is A=πr2

which would be 3.14 x 1^1 = 3.14

you take the diameter and square it and then multiply it by pi

Answer:

D. He answers the same number of questions correctly in both rounds and the same number of questions incorrectly in both rounds​.

Step-by-step explanation:

In the first equation he earns 5 points and loses 3 points. The value of one question is 5 points, and the value of losing one question is 3 points. The same goes for the second equation except the fact that its 10 points and 4 points lost instead.