Which choices are equivalent to the expression below? Check all that apply. 3√6 A. √27•√2 B. √18 C. 54 D. √54 E. √27•√4 F. √9•√6​

Answer:

the probability is 4.6%

Given:

The preimage and image of a triangle in the given figure.

To find:

The dilation scale factor.

Solution:

From the given figure it is clear that the vertices of the triangle ABC are A(-2,-2), B(-1,2) and C(2,1).

The vertices of the triangle A'B'C' are A'(-4,-4), B'(-2,4) and C'(4,2).

If a figure is dilated by factor K with (0,0) as the center of dilation, then

\((x,y)\to (kx,ky)\)

Let the scale factor be K, then the image of point A is:

\(A(-2,-2)\to A'(k(-2),k(-2))\)

\(A(-2,-2)\to A'(-2k,-2k)\)

From the given figure it is clear that the image of point A is A'(-4,-4).

\(A'(-2k,-2k)=A'(-4,-4)\)

On comparing both sides, we get

\(-2k=-4\)

\(k=\dfrac{-4}{-2}\)

\(k=2\)

Therefore, the dilation scale factor is 2.

Answer: 6.4

Step-by-step explanation:

divide in half

Answer:

8 \(\frac{1}{6}\)

Hope this helps.

The mass of an object will be same as the total sum of its parts or pieces.

For example :

The mass of a whole pizza is 500 grams, If you divide it into half.

The mass of each half pizza will be 250 grams each.

The total mass of two half pizzas is 250 + 250 = 500 grams which is the same as the mass of the whole pizza.

So the correct answer is :

The total mass of all the pieces together will be "Equal to the original mass of the object".

To find the range of the function f(x) = √x - 7, we need to consider the domain of the function, which is the set of all possible input values that we can use in the function. Since the square root of a number must be non-negative, the domain of this function is x ≥ 49.

Next, we need to evaluate the function for different values of x within the domain to see what values it produces. For example, if we plug in x = 49, we get f(49) = √49 - 7 = 7 - 7 = 0. If we plug in x = 50, we get f(50) = √50 - 7 = 7.236 - 7 = 0.236. As we can see, the function takes on both positive and negative values within its domain, so the range is all real numbers.

To represent this visually, we can plot the function on a graph and see how its values vary as the input x changes. We can use a graphing calculator or other graphing technology to do this. On a graph, the x-axis represents the input values (the domain of the function), and the y-axis represents the output values (the range of the function).

Here is a graph of the function f(x) = √x - 7:

[Insert graph here]

As we can see from the graph, the range of the function is all real numbers, indicated by the fact that the graph extends to both positive and negative infinity on the y-axis. This tells us that the range of the function is {y | y ∈ ℝ}.

Answer:

\((x-5)^2+(y-7)^2=50\)

Step-by-step explanation:

Hi there!

Equation of a circle: \((x-h)^2+(y-k)^2=r^2\) where the circle is centered at \((h,k)\) and r is the radius

Plug in the center (5,7)

\((x-5)^2+(y-7)^2=r^2\)

Plug in the given point (-2,8) to solve for r²

\((-2-5)^2+(8-7)^2=r^2\\(-7)^2+(1)^2=r^2\\49+1=r^2\\50=r^2\)

Therefore, r² is equal to 50. Plug this back into \((x-5)^2+(y-7)^2=r^2\)

\((x-5)^2+(y-7)^2=50\)

I hope this helps!

Morgan will need approximately 9.82 square feet of fabric to cover the cushions.

To find the total square footage of fabric needed to cover the cushions, we first need to calculate the area of each circular cushion and then multiply it by the number of cushions.

The formula for the area of a circle is A = πr², where A is the area and r is the radius. However, we don't have the radius directly, only the circumference.

The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. Rearranging this equation, we can find the radius in terms of the circumference: r = C / (2π).

Let's calculate the radius of each cushion using the given circumference:

C = 7.85 feet

r = C / (2π) = 7.85 / (2 × 3.14) ≈ 1.25 feet

Now we can calculate the area of each cushion:

A = πr² = 3.14× (1.25)² ≈ 4.91 square feet

Since there are two cushions, we need to double this area:

Total area needed = 2 × 4.91 square feet = 9.82 square feet

Therefore, Morgan will need approximately 9.82 square feet of fabric to cover the cushions.

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Answer:

m∠C = 102°

Step-by-step explanation:

This diagram is a Quadrilateral inscribed in a circle

The first step is to determine what m∠B

is

The sum of opposite angles in an inscribed quadrilateral is equal to 180°

m∠D + m∠B = 180°

m∠B = 180° - m∠D

m∠B = 180° - 80°

m∠B = 100°

Second step is we proceed to determine the exterior angles of the circle

m∠ADC = 2 × m∠B

m∠ADC = 2 × 100°

m∠ADC = 200°

m∠ADC = m∠CD + m∠AD

m∠AD = m∠ADC - m∠CD

m∠AD = 200° - 116°

m∠AD = 84°

The third step is to determine m∠BAD

m∠BAD = m∠AD + m∠AB

m∠BAD = 84° + 120°

m∠BAD = 204°

The final step Is to determine what m∠C is

It is important to note that:

m∠BAD is Opposite m∠C

Hence

m∠C = 1/2 × m∠BAD

m∠C = 1/2 × 204

m∠C = 102°

0.7 bar can be expressed as 7/9 in fraction.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.

In mathematics, a fraction is referred to as a portion of a whole. For instance, if a pizza is cut into four equal pieces, each one is represented by a quarter. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers.

Part of a whole number and a means of dividing a number into equal parts are represented by fractions. The numerator, also known as the number of equally divided parts, is how it is written.

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Answer:

the answer is c I believe

Step-by-step explanation:

5(10) 50 + 25 is 75 equals 25 and 10 + 5 is 15 so 75 + 15 is 90. so the answer is c

In the parallelogram BCDE, the measure for ∠CBE is evaluated to be 123°.

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

A parallelogram BCDE is given.

A diagonal BD is drawn.

The measure of ∠BDC = 68°.

The measure of ∠BCD = (2x + 57)°.

The measure of ∠BDE = (x + 55)°.

According to the properties of a parallelogram opposite interior angle are equal which gives -

∠BDC = ∠DBE = 68°

∠BDE = ∠DBC = (x + 55)°

Another property of parallelogram states that the adjacent angles of the parallel sides of the parallelogram form an angle sum of 180°.

This can be mathematically represented as -

∠EBC + ∠BCD = 180°

(∠DBE + ∠DBC) + ∠BCD = 180°

Substitute the values into the equation -

[68° + (x + 55)°] + (2x + 57)° = 180°

Solving the equation we get -

(123° + x) + (2x + 57)° = 180°

180° + 3x = 180°

x = 1/3

Substitute the value of x in ∠DBC -

∠DBC = 1/3 + 55°

∠DBC = 55°

So, the measure of ∠CBE = ∠DBE + ∠DBC

∠CBE = 68° + 55°

∠CBE = 123°

Therefore, the value for ∠CBE is obtained as 123°.

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3x-12y=6

Lets convert to slope intercept form

Slopes are equal so lines are parallel

Hence no solutions

This question requires estimating the probability of various occurrences related to the roll of two dice, one red, and one blue. The occurrences A, B, and C occur when the sum of the two dice is even, when the sum is at least 10, and when the red die comes up 5, respectively. Calculating the likelihood of each individual event, as well as conditional probabilities, and distinguishing independent pairs of occurrences are all part of the process.

(a) Probability of each individual event is as follows:

P(A) = probability of an even sum = (number of favorable outcomes)/(number of possible outcomes)= 18/36 = 1/2

P(B) = probability of a sum at least 10= (number of favorable outcomes)/(number of possible outcomes) = 3/36= 1/12

P(C) = probability of red die shows 5 = (number of favorable outcomes)/(number of possible outcomes) = 1/6

(b) P(A|C) = probability of getting an even sum on the dice given that the red die shows 5= (number of favorable outcomes)/(number of possible outcomes)

Since we know that the red die shows 5, there are three favorable outcomes to getting an even sum: (4, 1), (4, 3), and (6, 5). The probability of one of these outcomes occurring is P(A|C) = 3/3 = 1

(c) P(B|C) = probability of getting a sum of 10 or more on the dice given that the red die shows 5= (number of favorable outcomes)/(number of possible outcomes). Since we know that the red die shows 5, there are no possible outcomes that will result in a sum of 10 or more. Thus, P(B|C) = 0

(d) P(A|B) = probability of getting an even sum on the dice given that the sum is at least 10 = (number of favorable outcomes)/(number of possible outcomes)We know that the only way to obtain a sum of 10 or more is to get a 5 and a 5 or a 6 and a 4. Out of these two possible outcomes, only one of them has an even sum: (6, 4). Therefore, the probability of getting an even sum given that the sum is at least 10 is: P(A|B) = 1/2

(e) To determine which pairs of events among a, b, and c are independent, we have to determine whether P(A) = P(A|C), P(B) = P(B|C) and P(A)P(B) = P(A∩B).- P(A) = 1/2, P(A|C) = 1, P(A) ≠ P(A|C), so events A and C are not independent.- P(B) = 1/12, P(B|C) = 0, P(B) ≠ P(B|C), so events B and C are not independent.- P(A)P(B) = (1/2)(1/12) = 1/24, P(A∩B) = 1/36 = P((6, 4)), P(A)P(B) ≠ P(A∩B), so events A and B are not independent.

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Answer:

36 points

Step-by-step explanation:

3x14 = 42

1x6 = 6

42-6 = 36

Hope that helps

Answer:

54 hope this helps

Hello

DEF and IKL , equilateral  =>

DE = 5x-12 = 3x-4

5x-3x= -4+12

2x= 8

x=4

DE = 5x-12 =  20-12 = 8

KL = 3x+24 = 10x+3

24 -3 = 10x-3x

21 = 7x

x= 21/7 = 3

KJ = 10x+3 = 30+3 = 33

Answer:
Cluster : 60,61,62,63
Gaps: 64,65 , 69,70
Outlier: 71
This is what I learned so don't blame me please!

Step-by-step explanation:

Cluster is numbers all on one side. Outlier can be the largest number or lowest. Normally the alone one.

log₂(7) + log₂(8) is equal to log₂(56).

Logarithmic is a mathematical concept that is used to describe the relationship between a number and its exponent. In particular, a logarithm is the power to which a base must be raised to produce a given number. For example, if we have a base of 2 and a number of 8, the logarithm (base 2) of 8 is 3, since 2 raised to the power of 3 equals 8.

Logarithmic functions are commonly used in mathematics, science, and engineering to describe exponential growth and decay, as well as to solve various types of equations. They are particularly useful in dealing with large numbers, as logarithms allow us to express very large or very small numbers in a more manageable way.

The logarithmic function is typically denoted as log(base a) x, where a is the base and x is the number whose logarithm is being taken. There are several different bases that are commonly used, including base 10 (common logarithm), base e (natural logarithm), and base 2 (binary logarithm). The properties of logarithmic functions, including rules for combining and simplifying logarithmic expressions, are well-defined and widely used in mathematics and other fields.

We can use the logarithmic rule that states that the sum of the logarithms of two numbers is equal to the logarithm of the product of the two numbers. That is,

log₂(7) + log₂(8) = log₂(7 × 8)

Now we can simplify the product of 7 and 8 to get:

log₂(7) + log₂(8) = log₂(56)

Therefore, log₂(7) + log₂(8) is equal to log₂(56).

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Answer:

1cm, 2.4cm, 2.6cm

Step-by-step explanation:

They have to follow the pythagorean theorem a^2+b^2=c^2.

1^2+2.4^2=2.6^2 so it follows the pythagorean theorem so these three squares would form a right triangle.

Using the sides of the squares C, A and E the right triangle can be formed.

The Pythagoras theorem, often known as the Pythagorean theorem, describes the relationship between a right-angled triangle's three sides. The hypotenuse of a triangle's square is equal to the sum of the squares of its other two sides, according to the Pythagoras theorem.

Given that, triangles can be created using the sides of squares.

By applying Pythagoras theorem,

2.6²=2.4²+1²

6.76=5.76+1

6.76=6.76

Therefore, using the sides of the squares C, A and E the right triangle can be formed.

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Answer:

The answer is 12.

Step-by-step explanation:

Let the smallest number = x and the largest number = x+2(since the three numbers are consecutive, we would have to use x+2. If we wanted the second largest number, it would be x+1)

We would write the statement "four times the smallest integer is equal to six more than more than three times the largest" as:

4x = 3(x+2) + 6

Now just solve.

4x = 3x+6+6     distributive property

4x = 3x+12        simplify

x  = 12               subtraction property

And since x is the smallest number, we have our answer.

Therefore, the answer is 12.

The tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.

What is Circle?

A circle is a two-dimensional geometric shape that is defined as the set of all points in a plane that are a fixed distance away from a given point, called the center of the circle. This distance is known as the radius of the circle.

A circle can also be defined as the locus of a point that moves in a plane in such a way that its distance from a fixed point is constant. The constant distance is the radius of the circle.

The minute hand on a clock makes a full rotation in 60 minutes, which means it travels the circumference of a circle with a radius of 23 cm in 60 minutes. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14.

Therefore, the circumference of the circle traced by the tip of the minute hand is:

C = 2πr = 2 × 3.14 × 23 cm ≈ 144.44 cm

To find out how far the minute hand travels in 11 minutes, we need to calculate what fraction of the circumference it covers in that time. Since 11 minutes is about 18.3% of an hour (60 minutes), the minute hand travels 18.3% of the circumference of the circle in that time:

Distance traveled = 0.183 × 144.44 cm ≈ 26.4 cm

Therefore, the tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.

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Answer:

the answers is 95 dollers

Cost of goods sold (COGS) is an important accounting calculation that measures the costs associated with selling a company’s goods or services. Therefore, the cost of goods sold for the month ended is $600.

Cost of Goods Sold (COGS) is a measure of the cost of goods sold during the accounting period. It is calculated by subtracting the beginning inventory from the cost of goods purchased during the accounting period and then adding the ending inventory. For Dig the Dogs, Inc., the cost of goods sold for the month ended is calculated as follows: Beginning Inventory = 0 Cost of Goods Purchased = $900 Ending Inventory = $300 .COGS = Beginning Inventory + Cost of Goods Purchased - Ending Inventory  = 0 + 900 - 300   = $600 Therefore, the cost of goods sold for the month ended is $600.

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Answer:

I hope this helps

Explanation:

The statistical measurement that informs a CTRS about how well the assessment results compare to what is being measured is Construct validity.

Construct validity assesses how well the assessment measures the intended construct or trait, and compares the results to other tests or measures of the same construct to determine how accurate and reliable the assessment is.

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Answer:

y=-4x-8

Step-by-step explanation:

use the equation y-y1=m(x-x1) and solve for y

Answer:

y=-4x-3

Step-by-step explanation:

For this, you would use the point-slope formula, which is (y-y1)=m(x-x1), with x1 and y1 being the coordinates from the ordered pairs, and m being the slope. You can plug the values from the problem into the formula:

(y-5)=-4(x+2)

y-5=-4x-8

y=-4x-3

hope this helps! :)

The expression of the quadratic function, f(x) = -2·x² - 8·x - 5, in the vertex form indicates;

(a) f(x) = -2·(x + 2)² + 3

(b) Please find attached the graph of the quadratic function, showing five points, including the vertex created with MS Excel

The vertex form of a quadratic function is the form, f(x) = a·(x - h)² + k, where;

(h, k) = The coordinates of the vertex

(a) f(x) = -2·x² - 8·x - 5

The function can be expressed in the vertex form as follows;

The vertex form is; f(x) = a·(x - h)² + k

f(x) = -2·x² - 8·x - 5 = -2·(x² + 4·x) - 5

f(x) = -2·(x² + 4·x) - 5

f(x) = -2·(x² + 4·x + 4 - 4) - 5

f(x) = -2·((x + 2)² - 4) - 5

f(x) = -2·((x + 2)² + 8 - 5

f(x) = -2·((x + 2)² + 3

The vertex of the quadratic function is; (h, k) = (-2, 3)

(b) The five points that can be used to plot the graph of the quadratic function can be obtained by considering the points with x-coordinates, -3, and -4, to the left of the vertex and -1, and 0 to the right of the vertex as follows;

f(-4) = -2·((-4) + 2)² + 3 = -5

f(-3) = -2·((-3) + 2)² + 3 = 1

f(-2) = -2·((-4) + 2)² + 3 = 3

f(-1) = -2·((-1) + 2)² + 3 = 1

f(0) = -2·((0) + 2)² + 3 = -5

Please find the graph of the quadratic function, f(x) = -2·(x + 2)² + 3, created with MS Excel

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a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

The disadvantages of cluster sampling are:

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

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We also know that 1 4 and 8 5 by the vertical angles theorem.

Vertical angles, also known as vertically opposite angles, are the opposing angles formed when two lines converge. Angles that are vertically opposite one another are always equal to one another. A vertical angle and the angle it is near to are also supplementary angles, which means their combined angle is 180 degrees.

The opposite angle, for example, is 45° when two lines intersect to form an angle, say X=45°. And the angle next to angle X will be 180 – 45, or 135 degrees.

Correct Question :

Given: e || f and g is a transversal.

Prove: 1 8 Given that e || f and g is a transversal, we know that 4 5 by the alternate interior angles theorem. We also know that 1 4 and 8 5 by the (corresponding angles theorem / alternate interior angles theorem / vertical angles theorem / alternate exterior angles theorem). Therefore, 1 8 by the transitive property.

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