can you rearrange negative & positive numbers? I know we're supposed to solve them from left to right, but

isn't 7-5 the same as -5+7? can't we rearrange them??

​

The test administered by Natalia to the job candidate is reliable.

Natalia administered a test to a job candidate three different times. The scores obtained by the candidate are 85, 87, and 85 out of 100. Natalia notes that the scores are fairly consistent. Therefore, the test is reliable.

A test is considered reliable if it produces consistent results over time. In this case, the scores obtained by the candidate are fairly consistent, indicating that the test is reliable.

Therefore, the correct answer is "reliable."

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The length of BC in this problem is given as follows:

BC = 3.6.

Two triangles are defined as similar triangles when they share these two features listed as follows:

The similar triangles for this problem are given as follows:

ABC and ADE.

Hence the proportional relationship for the side lengths is given as follows:

3/5 = BC/6.

Applying cross multiplication, the length BC is given as follows:

BC = 6 x 3/5

BC = 3.6.

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Answer:

1. no 2: yes 3: yes 4. no 5.no 6. no

Step-by-step explanation:

We can use the fact that 32 is equal to 2 raised to the power of 5:

32 = 2^5

Substituting this into the equation gives:

16^x = 2^5

We can then rewrite 16 as 2^4, since 16 is equal to 2 raised to the power of 4:

(2^4)^x = 2^5

Simplifying the left side of the equation gives:

2^(4x) = 2^5

Now we can see that the bases of both sides of the equation are equal, so we can set the exponents equal to each other:

4x = 5

Dividing both sides by 4 gives:

x = 5/4

Therefore, the solution to the equation 16^x = 32 is x = 5/4.

The number of possible license plates in this scenario is 6,760,000.

This is because there are 26 letters in the alphabet and the state uses two letters for the license plate, so there are 26 options for the first letter and 26 options for the second letter.

This gives a total of 26 x 26 = 676 possible letter combinations. Then, the state uses four-digit integers which can range from 0000 to 9999, so there are 10 options for each of the four digits. This gives a total of 10 x 10 x 10 x 10 = 10,000 possible number combinations.

Therefore, the total number of possible license plates is 676 x 10,000 = 6,760,000.

Each character in the license plate is independent of the others, so the number of different license plates possible is the product of the number of choices for each character.

In this case, there are 26 choices of letters for the first character, 26 choices of letters for the second character, 10 choices of digits for the third character, and 10 choices of digits for the fourth character.

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Answer:

The interest will rack up to $7,200

The total will be $15,200

Step-by-step explanation:

the interest she pays is $7,000

the total amount she pays is $15,200

Jenna borrows $8,000 for college at a simple interest rate of 6%

she has 15 years to pay back the loan and interest

the interest can be calculated as follows

= 6/100 × 8,000

= 0.06 × 8000

= 480

= 480 × 15

= $7200

the total amount she pays can be calculated as follows

= $7200 +$8000

= $15,200

Hence the interest she pays is $7200 and the total amount is $15,200

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a) The area of triangle PQR is:

Area = √(6)/2

b) The equation of the plane that contains P, Q, and R is:

x + y + 2z = 2

a) For the area of the triangle PQR, we can use the formula:

Area = 1/2 |PQ x PR|

where PQ and PR are the vectors from P to Q and R, respectively, and x denotes the cross product.

So, we have:

PQ = <1-0, -1-0, 2-1> = <1, -1, 1>

PR = <-1-0, 1-0, 1-1> = <-1, 1, 0>

Taking the cross product:

PQ x PR = <1, -1, 1> x <-1, 1, 0> = <-1, -1, -2>

Taking the magnitude:

|PQ x PR| = √((-1)² + (-1)² + (-2)²) = √(6)

So, the area of triangle PQR is:

Area = 1/2 × √(6) = √(6)/2

b) To find the equation of the plane that contains P, Q, and R, we can use the point-normal form of the equation:

n · (r - P) = 0

where n is the normal vector of the plane (which is perpendicular to the plane), r is any point on the plane, and · denotes the dot product.

To find the normal vector, we can take the cross product of PQ and PR:

n = PQ x PR = <-1, -1, -2>

Now, we can use any of the three points to find the equation of the plane. Let's use P:

n · (r - P) = 0

Substituting n and P:

<-1, -1, -2> · (r - <0, 0, 1>) = 0

Expanding the dot product:

-1(r_x - 0) - 1(r_y - 0) - 2(r_z - 1) = 0

Simplifying:

-r_x - r_y - 2r_z + 2 = 0

So, the equation of the plane that contains P, Q, and R is:

x + y + 2z = 2

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The first one on the left.

The vertical bars mean we take the absolute value of that number.

Absolute value means distance from zero on a number line.

So the absolute value of any number

is the positive version of that number.

So for the one on the left we have |-100| > |50|.

Since absolute value represents the positive version

of a number, the absolute value of -100 will be 100.

Since |50| is already positive, it stays the same.

So we have 100 > 50 which is indeed a true statement.

If you solve the other ones, you will see that they are false.

Answer:

the first one on the left side

Step-by-step explanation:

Answer:

\(6x = 4x + 6 \\ 6x - 4x = 6 \\ 2x = 6 \\ x = \frac{6}{2} \\ \boxed{x = 3}\)

Answer:

x = 3

Step-by-step explanation:

In pic

(Credits: Symbolab)

(Hope this helps can I pls have brainlist (crown)☺️)

The polynomial function is the product of two different linear factors, (x-2) and (x+3)^2, which means that we have two different roots, x=2 and x=-3

A polynomial function is a function that can be written as constants and n is the degree of the polynomial. The polynomial function y = (x − 2)(x + 3)² is a quadratic function because it has an \(x^{2}\) term.

The roots of a polynomial function are the values of x that make the function equal to zero. In other words, they are the solutions to the equation y = 0.

The polynomial function y = (x − 2)(x + 3)² can be factored as (x-2)(x+3)(x+3), which means that we have three different linear factors, (x-2), (x+3), and (x+3) . Each linear factor corresponds to one root of the polynomial.

So the polynomial function y = (x − 2)(x + 3)² has 2 distinct roots. The correct answer is C.

Alternatively, we can also see that the polynomial function is the product of two different linear factors, (x-2) and \((x+3)^{2}\), which means that we have two different roots, x=2 and x=-3.

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The temperature at which it was steady was 65°F.

We are given the graph of temperature in degree Fahrenheit on the y-axis against time on the x-axis.

Now, we see that the graph curve was increasingly accelerating up to a temperature of approximately 65°F.

Now, at the temperature of 65°F, the temperature remained steady for a time period of about 3 hours from 3pm to 6pm.

Thus, we conclude that the temperature at which it was steady was 65°F.

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The coordinates of A'', B'' and C'' are (-1, 4), (-4, 3) and (-1, 2) respectively.

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

Given triangle has coordinates,

A(2, -2), B(5, -3) and C(2, -4).

First the triangle is translated by the rule (x, y) → (x - 1, y + 6)

A(2, -2) becomes A'(2 - 1, -2 + 6) = A'(1, 4).

B(5, -3) becomes B'(5 - 1, -3 + 6) = B'(4, 3)

C(2, -4) becomes C'(2 - 1, -4 + 6) = C'(1, 2)

Then the translated triangle is reflected across the Y axis.

When reflected a point (x, y) across the Y axis, y coordinate remains same and x coordinate flips.

A'(1, 4) becomes A''(-1, 4)

B'(4, 3) becomes B''(-4, 3)

C'(1, 2) becomes C''(-1, 2)

Hence the vertices of the triangle after undergoes translation and reflection becomes A''(-1, 4), B''(-4, 3) and C''(-1, 2).

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1. The ratio of shirts Pete pays for to all shirts is 1000.

2. Pete would pay Ana $8.33 for each shirt.

3. Pete would pay Jun $9600 for the shirt.

To determine what Pete would pay Ana for the shirts, we can use the "Buy 5, Get 1 Free" discount. The ratio of shirts Pete pays for to all the shirts Pete gets is 5:6 (5 shirts paid, and 1 shirt received for free).

To fill in the statements:

1. The ratio of shirts Pete pays for to all the shirts Pete gets is 5:6 of 1200 is ____.

To find the missing value, we can set up the following equation:

5/6 * 1200 = x

Solving for x, we have:

x = (5/6) * 1200 = 1000

So, the ratio of shirts Pete pays for to all the shirts Pete gets is 5:6 of 1200 is 1000.

2. ___ × $10 = $

Pete pays $10 for each shirt. Since the ratio is 5:6, the missing value can be calculated as follows:

5/6 * $10 = $8.33 (rounded to two decimal places)

Therefore, Pete would pay Ana $8.33 for each shirt.

3. What would Pete pay Jun for the shirt?

Pete would pay Jun $8 for each shirt. Since Pete needs 1200 shirts, we can calculate the total amount he would pay Jun as follows:

1200 x $8 = $9600

Therefore, Pete would pay Jun $9600 for the shirts.

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Answer:

3\(\sqrt{2}\)

Step-by-step explanation:

Use the pythagorean method: a^2 + b^2 = x^2. Your a and b are both 3, and your c is x, so...

3^2 + 3^2 = x^2

9 + 9 = x^2

18 = x^2

\(\sqrt{18}\) = x

(18 = 2 * 3 * 3, 3 has a pair, take that out)

3\(\sqrt{2}\) = x

Answer:

\(3\sqrt{2}\)

Step-by-step explanation:

\(x^{2} = 3^{2} +3^{2} \\x^{2} = 9+9\\x^{2} = 18\\x= \sqrt{18} \\x= \sqrt{9*2} \\x=3\sqrt{2}\)

The option that is not characteristic of the t-test is "The Student t distribution has mean of t = 0 and a standard deviation of 5 = 1". The correct answer is option A.

The t-test is a statistical test that uses the Student t-distribution. The Student t-distribution has a mean of 0, but its standard deviation is not equal to 1. The standard deviation of the t-distribution varies depending on the degrees of freedom, which is determined by the sample size. Therefore, the statement in option A is not true. The correct answer is option A.

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Answer:

C is the answer!

Step-by-step explanation:

The angle (in radians) between vectors u and v is approximately 1.66 radians, rounded to two decimal places.

To find the angle between two vectors, we can use the dot product formula and the magnitudes of the vectors. Let's calculate the angle between vectors u and v:

Given:

u = 4i - 6j

v = 5i + 4j

Step 1: Calculate the dot product of u and v.

The dot product of two vectors u and v is given by:

u · v = |u| |v| cosθ

where |u| and |v| are the magnitudes of vectors u and v, respectively, and θ is the angle between them.

To calculate the dot product, we multiply the corresponding components of u and v and sum them:

u · v = (4 * 5) + (-6 * 4) = 20 - 24 = -4

Step 2: Calculate the magnitudes of vectors u and v.

The magnitude of a vector is given by:

|u| = √(u₁² + u₂²)

For vector u:

|u| = √((4)² + (-6)²) = √(16 + 36) = √52 ≈ 7.21

For vector v:

|v| = √((5)² + (4)²) = √(25 + 16) = √41 ≈ 6.40

Step 3: Calculate the angle θ.

Using the dot product formula mentioned earlier, we have:

-4 = (7.21)(6.40)cosθ

Solving for cosθ:

cosθ = -4 / (7.21 * 6.40) ≈ -0.086

To find θ, we can take the inverse cosine (arccos) of cosθ:

θ ≈ arccos(-0.086) ≈ 1.66 radians

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1. Independent random samples arise when one random sample is split into groups differing by an observed feature is incorrect.

2. The margin of error of a confidence interval about the difference between the means of two populations is equal to half the width of the confidence interval.

1. Independent random samples arise when individuals in a sample are randomly assigned to experimental groups, data is recorded repeatedly on a random sample of individuals, or random samples are selected separately. The statement that one random sample is split into groups differing by an observed feature does not accurately describe independent random samples.

2. The margin of error in a confidence interval represents the range of values within which the true population parameter is likely to fall. It is calculated by taking half of the width of the confidence interval. Therefore, the correct answer is that the margin of error is equal to half the width of the confidence interval.

In summary, the incorrect statement is that independent random samples arise when one random sample is split into groups differing by an observed feature. The margin of error of a confidence interval about the difference between the means of two populations is equal to half the width of the confidence interval.

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Answer:

Answer is below

Step-by-step explanation:

To solve this, you can set up an equation. Make the length of the shortest side x, so the 2 sides double the length will equal 2x. Since they all equal the perimeter of 36, do x + 2x + 2x =36. These values all represent the sides(2 longer, one short). Combine like terms to get 5x=36 then divide by 5 to find the value of x. x=7.2in meaning the shorter side is 7.2 inches while the longer sides are both 14.4 inches each since they are double in size.

Answer:

D:X+2X+2X=36

Step-by-step explanation:

X+X=EQUAL AND DOUBLE THE SHORTEST SIDE

2[X+X]+[X]=36

Answer:

$72

Step-by-step explanation:

im guessing

To find the volume of the solid generated by revolving the region between y = x^2 and y = 12 - x about the line y = -2, we can use the disk/washer method by integrating the difference between the functions squared over the interval of intersection.

To find the volume of the solid generated by revolving the region bounded by y = x^2 and y = 12 - x about the horizontal line y = -2, we can use the disk/washer method.

First, let's find the points of intersection between the two curves:

x^2 = 12 - x

Rearranging the equation:

x^2 + x - 12 = 0

Factoring the quadratic equation:

(x - 3)(x + 4) = 0

So, the points of intersection are x = 3 and x = -4.

To use the disk/washer method, we need to integrate over the interval [-4, 3].

The radius of each disk or washer is given by the difference between the functions:

r = (12 - x) - x^2

The volume element can be expressed as:

dV = πr^2 dx

Integrating the volume element over the interval [-4, 3]:

V = ∫[-4,3] π((12 - x) - x^2)^2 dx

Evaluating this integral will give us the volume of the solid.

Note: The washer method is used when the region between the curves is revolved around a horizontal or vertical axis, and the disk method is used when the region below the curve is revolved around a horizontal or vertical axis. In this case, we are revolving the region between the curves, so we use the washer method.

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We can create three functions related to the manufacturing of acrylic cylinders: V(r), which calculates the volume of water based on the radius of the cylinder; M(V), which calculates the mass of water based on the volume; and a composite function that combines the two. The composite function will take the radius of the cylinder as the input and provide the mass of the water in the cylinder as the output. These functions can be expressed in terms of pi and the given density of water (28 grams per cubic meter).

To explain the functions, let's start with V(r). Since the height of the cylinder is always twice the radius, we can express the volume using the formula for the volume of a cylinder: V(r) = pi * r^2 * h. Substituting the relationship between the height and radius, the formula simplifies to V(r) = pi * r^2 * (2r), which further simplifies to V(r) = 2pi * r^3.

Next, we have M(V) to calculate the mass of water based on the volume. Since the density of water is approximately 28 grams per cubic meter, we can express the mass as M(V) = V * density. Substituting the value of V from the previous function, we get M(V) = (2pi * r^3) * 28.

Finally, the composite function takes the radius of the cylinder as the input and provides the mass of water in the cylinder as the output. Therefore, the composite function can be written as M(r) = (2pi * r^3) * 28, where M(r) represents the mass of water in the cylinder given the radius r.

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Answer:

Hypotenuse

Step-by-step explanation:

The longest side of a triangle is opposite the largest angle, which is the right angle in a right triangle.

Answer:

Hypotenuse.

Step-by-step explanation:

Discussion

A: says it is a right angle. It can't be the answer to the longest side.

B: Usually B and A might be the hypotenuse, but that is generally not the way they are displayed.

C: Neither B nor A can be chosen.

D: Answer:

(x - (a+48))² + (y - (b+19))² = 24.5² This is the equation for all possible positions (x,y) on the boundary of the cell tower's service coverage.

To write an equation for all possible positions (x,y) on the boundary of the cell tower's service coverage, we first need to determine the coordinates of the center of the coverage.

We know that the cell tower is located 48 miles east and 19 miles north of the center of the small town, so we can add these distances to the coordinates of the town's center. If we let (a,b) be the coordinates of the town's center, then the coordinates of the cell tower would be (a+48,b+19).

Next, we know that the cell tower services everything within a radius of 24.5 miles from it. This means that any point (x,y) on the boundary of the coverage circle would be exactly 24.5 miles away from the cell tower. We can use the distance formula to write an equation for this:

√[(x - (a+48))² + (y - (b+19))²] = 24.5

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Answer:

34

Step-by-step explanation:

Plugin 12 for x

f(12)=4+2.5(12)

2.5 times 12=30

30+4=34

step one it says Jasmine ran 22 km is approximately equal to 1.6 km in which measurement is closest to the number of miles Jasmine ran the correct answer is C

Answer:

D. (0, -1)

Step-by-step explanation:

Answer:

D. (0, -1)

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

10c - 7 • 11

c = 9

then:

= (10·9) - (7·11)

= 90 - 77

= 13

Answer:

Step-by-step explanation:

For two angles x and y to be supplementary, the sum of the angles must be 180°

x+y = 180

x = 180-y... 1

If the measure of the angle is five times greater than its supplement this is expressed as:

x = 5y…. 2

Substitute equation 2 into 1

5y = 180-y

5y+y = 180

6y = 180

y = 30°

Hence the measure of the supplement is x = 5y

x = 5(30)

x = 150°