The number of freshmen entering college in a certain year is 621. What type of data is 621?
Continuous data
Categorical data
Discrete data

Answer:

The answer is A

Step-by-step explanation:

Answer:

26 is the answer

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Given equation is [tex]f(x)= x(x+1)^2 (2x-3)(x+2)^2[/tex].

Now we need to find about what is the degree of the give function.

We know that degree of polynomial function is the highest exponent of the variable (x).

So we can either expand the whole equation or count the degree of each factor then add those to get the degree of the given function.

Second choice will be easier.

Degree of [tex]x[/tex] = 1

Degree of [tex](x+1)^2[/tex] = 2

Degree of [tex](2x-3)[/tex] = 1

Degree of [tex](x+2)^2[/tex] = 2

Hence degree of the given polynomial function = 1+2+1+2=6

Answer:

Do you mean like a "degree" of a circle?

Step-by-step explanation:

Answer:

Are you talking about the degrees of a circle?

Step-by-step explanation:

D. Shifted 4 units left and 2 units down

The answer to your problem is d.

Answer:

9m

Step-by-step explanation:

The surface area of a cube is given by

SA = 6s^2  where s is the side length

We know the surface area is 486 and the side length is z

486 = 6z^2

Divide each side by 6

486/6 = 6z^2/6

81 = z^2

Take the square root of each side

sqrt(81) = sqrt(z^2)

9 = z

Each side has a length of 9m

Answer:

Step-by-step explanation:

[tex]\dfrac{5^{11}}{5^x}=5^4\qquad\text{multiply both sides by}\ 5^x\\\\5^{11}=5^4\cdot5^x\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\5^{11}=5^{4+x}\iff11=4+x\qquad\text{subtract 4 from both sides}\\\\11-4=4-4+x\\\\7=x\to x=7[/tex]

Answer:

Center: (0,0)

Radius: [tex]r=\sqrt{10}[/tex]

Step-by-step explanation:

The given circle has equation

[tex]10x^2+10y^2=100[/tex]

In order to complete the square, we must make sure the coefficient of the quadratic terms are unity.

We divide through by 10 to obtain;

[tex]x^2+y^2=10[/tex]

The coefficient of the linear terms of both variables are zero.

Therefore the equation can be rewritten as;

[tex](x-0)^2+(y-0)^2=10[/tex]

Comparing to [tex](x-h)^2+(y-k)^2=r^2[/tex]

We have (h,k)=(0,0) to the center of the circle and [tex]r=\sqrt{10}[/tex] to be the radius of the circle.

Answer:

Equation: x²  + y² = 10

center = (0, 0)

  radius = √10

Step-by-step explanation:

The general equation of a circle is ;

(x - a)²  + (y - b)² = r²

Where (a, b) is the coordinate of the center of the circle, and r is its radius.

Where the center is (0,0), the equation becomes,

x²  + y² = r²

In our case we have;

10x² + 10y² = 100

dividing both side by ten,

x²  + y² = 10

∴ center = (0, 0)

  radius = √10

Answer:

-61

Step-by-step explanation:

-42-34=-76= -61

Answer:

the answer is 715

Step-by-step explanation:

Answer:

715

Step-by-step explanation:

5*100

5*40

5*3

then add all together

Make sure to use order of operations

Your answer is D. 2 seconds because her distance from the floor is consistent. Every push-up is 2 seconds apart, therefore it’s D.

Answer:

y = 4(2^x)

Step-by-step explanation:

To write the exponential values, compare the y values. Notice they are multiples of 8 and they are increasing. This means the base is likely 2 or 4 since each of these numbers has the same multiples. Our options also only include base 2 and 4.

Try 4^1 = 4 and 4^4 = 256.

Try 2^1 = 2 and 2^4 = 16.

None of these give the exact values in the points. This means there is an initial value multiplied to them as well.

When x = 1 and the base is 4, the value is too small. But when x = 4, the value is too large. This cannot be reconciled.

When x = 1 and x = 4 for the base 2, both values are too small and could be multiplied by the same number to get the right values.

2*4 = 8

16*4 = 64

The initial value is 4 so the function is [tex]y = 4(2^x)[/tex]

Answer:

$35.97

Step-by-step explanation:

the regular price is 59.95

40% discount so

let's say the price now is x and i am gonna do fractions

x/59.95 = 40%/100

100 x X = 100x  

59.95 x 40 = 2398

i divide 2398 by 100 which equal 23.98

40% is 23.98 and then i do 59.95 - 23.96 = 35.97

DONE!

The discount amount on the watch is $23.98 and the sale price after applying the 40% discount off the regular price of $59.95 is $35.97.

When a jewelry store is having a going-out-of-business sale, and all merchandise is marked 40% off the regular price, we can calculate the amount of the discount and the sale price using percentage formulas. For example, if a watch has a regular price of $59.95, we multiply this price by 40% (or 0.40) to find the discount amount.
To find the discount amount: $59.95 times 0.40 = $23.98

Next, to find the sale price, we subtract the discount amount from the regular price.
To find the sale price: $59.95 - $23.98 = $35.97

Therefore, the discount amount is $23.98, and the sale price of the watch is $35.97.

To solve divide both sides by 4 to cancel out the 4 on the x side to get x alone. Then just do -10/4. That gives you 2.5 so (X=2.5). Hope I helped and have a great day and night

Answer:

-5/2

Step-by-step explanation:

We start with 4x = -10 and want to solve this for x.

We divide both sides by 4 (which isolates x), obtaining:

x = -10/4

and then we reduce this to x = -5/2.

Answer:

(x-3)²

Step-by-step explanation:

x²-6x+9

x² can be written as (x)²

9 can be written as 3²

(x)²-6x +(3)

we can break 6x as 2(3)(x)

by using square formula

(a+b)²= a²-2ab+b²

Putting all the values back in expression we get

(x)²-2(3)(x)+(3)²

by closing formula we get

(x-3)²

Answer:

(x-3)2

Step-by-step explanation:

i took the test

Answer:

Answer: 572

Step-by-step explanation:

Answer:

Answer:

y=−4x is a direct variation with the constant of variation +(−4)

Any equation in (or modifiable into) the form y = a . x

is a direct variation with constant a

Step-by-step explanation:

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (5, 20) and (7, 22). Substitute:

[tex]m=\dfrac{22-20}{7-5}=\dfrac{2}{2}=1[/tex]

[tex]y-20=1(x-5)[/tex]

[tex]y-20=x-5[/tex]         add 20 to both sides

[tex]y=x+15[/tex]

Answer:

No, because the median test score decreased 5 points.

Step-by-step explanation:

The middle line is is the median so, if the pre-test is 60 and the post-test is 55 then there is a 5 point difference.

The difference is [tex]\( \frac{5x^2 + 6x + 12}{(x-3)(x+2)(x+2)} \)[/tex].

To subtract the two rational expressions [tex]\( \frac{5x}{x^2-x-6} \) and \( \frac{4}{x^2+4x+4} \)[/tex], we need to find a common denominator.

First, factor the denominators:

1. x²-x-6 = (x-3)(x+2)

2. x²+4x+4 = (x+2)²

The common denominator will be (x-3)(x+2)(x+2).

Now, rewrite the expressions with the common denominator:

1. [tex]\( \frac{5x}{(x-3)(x+2)} \)[/tex]

2. [tex]\( \frac{4}{(x+2)^2} \)[/tex]

To subtract, the numerators remain the same, so the expression becomes:

[tex]\[ \frac{5x}{(x-3)(x+2)} - \frac{4}{(x+2)^2} \][/tex]

To combine the fractions, we need to rewrite the first fraction with the common denominator:

[tex]\[ \frac{5x(x+2)}{(x-3)(x+2)(x+2)} - \frac{4(x-3)}{(x-3)(x+2)(x+2)} \][/tex]

Now, we can subtract the fractions:

[tex]\[ \frac{5x(x+2) - 4(x-3)}{(x-3)(x+2)(x+2)} \\\[ = \frac{5x^2 + 10x - 4x + 12}{(x-3)(x+2)(x+2)} \\\[ = \frac{5x^2 + 6x + 12}{(x-3)(x+2)(x+2)} \][/tex]

So, the difference is [tex]\( \frac{5x^2 + 6x + 12}{(x-3)(x+2)(x+2)} \)[/tex].

To find the difference between the two rational expressions, we first need to factorize the denominators and simplify where possible. Let's break it down step by step:

1. Factorize the denominators:

[tex]\(x^2 - x - 6 = (x - 3)(x + 2)\) \(x^2 + 4x + 4 = (x + 2)^2\)[/tex]

2. We rewrite the expressions with common denominators:

  [tex]\(\frac{5x}{(x - 3)(x + 2)} - \frac{4}{(x + 2)^2}\)[/tex]

3.  To simplify these, we need a common denominator, The least common denominator is [tex]\((x - 3)(x + 2)^2\).[/tex], so to get it, we multiply (x + 2) with Expression 1 and  (x - 3) with Expression 2 on both numerator and denominator. We get:

  [tex]\(\frac{5x(x + 2)}{(x - 3)(x + 2)^2} - \frac{4(x - 3)}{(x - 3)(x + 2)^2}\)[/tex]

4. We combine the fractions:

[tex]\(\frac{5x(x + 2) - 4(x - 3)}{(x - 3)(x + 2)^2}\)[/tex]

  [tex]\(= \frac{5x^2 + 10x - 4x + 12}{(x - 3)(x + 2)^2}\) \(= \frac{5x^2 + 6x + 12}{(x - 3)(x + 2)^2}\)[/tex]

So, the difference between the two rational expressions is [tex]\(\frac{5x^2 + 6x + 12}{(x - 3)(x + 2)^2}\).[/tex]

Martha walked for 0.67 hours.

Here's how we can calculate it:

Total time spent hiking:

12:30 AM - 11:30 PM = 1 hour (since 12:30 AM is midnight and the same as 00:30 AM)

Convert hours to minutes: 1 hour * 60 minutes/hour = 60 minutes

Time spent running:

Subtract the walking time from the total time: 60 minutes - 20 minutes = 40 minutes

Convert running time to hours:

Divide minutes by minutes per hour: 40 minutes / 60 minutes/hour = 0.67 hours

Therefore, Martha walked for 0.67 hours.

Question

If Martha went on a hiking trip at 11:30 PM, and walked for 20 minutes, and ran the rest, and came back at 12:30 AM, how many hours did Martha WALK?

The equation x + y = 10 represents a linear relationship that spans all real numbers in both x and y directions. Thus, the domain and the range for this function are both all real numbers.

The equation for the set F is x + y = 10, which is a straight line on a graph. This line extends infinitely in both directions, meaning that there is no restriction on the possible values of x (the domain) and y (the range). Therefore, the correct answer for both domain and range would be 'All Real Numbers'.

To visualize this, imagine you plug in any number for x and solve the equation for y. Similarly, you can do the same, guessing a y-value and solving for x. No matter the number chosen, there will always be a corresponding number on the other side, whether positive, negative, or zero.

Remember that a domain is the set of all inputs (or 'x' values) that a function can accept, and a range is the set of all possible outputs (or 'y' values) that the function can produce. In this example, the function can handle and generate all real numbers, so its domain and range are all real numbers.

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Answer:

The volume of a rectangular prism is [tex]28\frac{7}{8}\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the rectangular prism is equal to

[tex]V=BHL[/tex]

Convert the given dimensions to an improper fractions

[tex]B=3\frac{1}{2}\ cm=\frac{3*2+1}{2}=\frac{7}{2}\ cm[/tex]

[tex]H=1\frac{1}{2}\ cm=\frac{1*2+1}{2}=\frac{3}{2}\ cm[/tex]

[tex]L=5\frac{1}{2}\ cm=\frac{5*2+1}{2}=\frac{11}{2}\ cm[/tex]

substitute in the formula

[tex]V=(\frac{7}{2})(\frac{3}{2})(\frac{11}{2})=\frac{231}{8}\ cm^{3}[/tex]

Convert to mixed number

[tex]\frac{231}{8}=\frac{224}{8}+\frac{7}{8}=28\frac{7}{8}\ cm^{3}[/tex]

Answer:

Broke paints [tex]216\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The area of the outsides of the square walls and triangular ceilings of her tree house is equal to the area of four squares and four triangles

so

[tex]A=4[(6)^{2} +\frac{1}{2}(6)(6)]\\ \\A=4[36+18]\\ \\A=216\ ft^{2}[/tex]

The surface area of the square walls and triangular ceiling she painted is 216 ft²

The surface area of the painted region can be found as follows:

area of the square = l²

where

Therefore,

l = 6 ft

area of the square = 6² = 36 ft²

Area of the triangular region = 1 / 2 bh

where

Therefore,

area of the triangular region = 1 /  2 × 6 × 6 = 36 / 2  = 18 ft²

Therefore,

area of the painted region = 18(4) + 36(4) = 144 + 72 = 216 ft²

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Answer :

D

Solution :

14ft + 17ft = 30ft

31ft = 30ft

well, in the election, the losing candidate received 10200 votes, and we know that's 30% of the whole votes cast, le's say the whole amount is "x" or namely 100%.

B)

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 10200&30\\ x&100 \end{array}\implies \cfrac{10200}{x}=\cfrac{30}{100}\implies \cfrac{10200}{x}=\cfrac{3}{10} \\\\\\ 102000=3x\implies \cfrac{102000}{3}=x\implies 34000=x[/tex]

A)

Dorian's 3060 is really 30% of 10200, however, the losing candidate received 30% of the total votes cast, and that is 10200, so Dorian mistakenly is using 30% of the 30% received by the losing candidate as point of reference for her total.

Final answer:

Dorian's claim is incorrect because dividing 10,200 votes by 30% (or 0.30) gives 34,000 votes, which is the correct total number of votes cast in the mayoral election. Therefore, the calculation shows that the total votes are much higher than Dorian's claim of 3,060 votes.

Explanation:

A. Dorian's claim that the total number of votes cast in the mayoral election was 3,060 is not reasonable because if the losing candidate received 10,200 votes which represented 30%, then the total votes should be much higher than 3,060. To find the total, you would divide the number of votes the candidate received by the percentage they represent.

B. To find the total number of votes cast in the mayoral election, you would set up the equation 10,200 = 0.30 * Total Votes. Dividing 10,200 by 0.30 gives the total number of votes cast, which is 34,000.

Equation: Total Votes = 10,200 votes / 0.30 = 34,000 votes

Answer:

It is the famous Pythagorean theorem which is this equation:

a^2 + b^2 = c^2,

where a and b are the legs and c is the hypotenuse.

Answer:

Pythagorean theorem

Step-by-step explanation:

Unfilled circle on 3, filled circle on 0, line connecting the circles.

•—————o

0 3

The values of x that have the absolute value less than 3 are plotted in the figure attached.

The number line should be represented in the straight line that have the zero point in the middle, having the positive and negative numbers that should be listed on the other side.

Given that to plot all values of x that have the absolute value less than 3,

It can be written as |x| ≤ 3

We can say that,

The values of x that have the absolute value greater than 3 are -3 and 3. It should be located into the equal intervals.

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Answer:

b

Step-by-step explanation:

➷ 40 + 25 = 65

75 - 65 = 10

The correct answer would be B. $10

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