Match each function with its range.

Answer:

61 hot dogs

122 sodas

Step-by-step explanation:

x+x2=183

3x=183

183÷3=

61

Answer: B

Step-by-step explanation:

Answer:

x = 110

Step-by-step explanation:

measure of abd is 35, meaning adb is also 35.

so dab + abd + adb is 180

=> x + 35 + 35 = 180

=> x + 70 = 180

=> x = 180-70

=> x = 110

110 degrees is the value of x.  

Answer: 921 bags

Step-by-step explanation:

      We will subtract bags used from the total number of bags.

953 - 32 = 921

        The bakery still has 921 bags of sugar.

Answer:

21.8 m/s

Step-by-step explanation:

Given that Tom drops a object from a height of h meters and it hits the ground with a veloc8of v m/s and it is given by function ;

[tex]\longrightarrow v =\sqrt{19.6h}[/tex]

We need to find out the velocity upon reaching the ground when it is dropped from a height of 24.3 m . On plugging in 24.3 in place of h we have ,

[tex]\longrightarrow v =\sqrt{19.6\times 24.3 }\ m/s\\\\\longrightarrow v =\sqrt{ 476.28} m/s \\\\\longrightarrow v = 21.823 \ m/s \\\\\longrightarrow \underline{\underline{ v = 21.8 \ m/s }}[/tex]

And we are done !

Answer:

21.8

Step-by-step explanation:

The formula is given :

Given that h = 24.3 m, we need to find v.

Substituting the value of h in the formula :

Answer:

KL = 32

Step-by-step explanation:

The triangle is equilateral.

Finding KL :

The probability that the first two songs played are slow songs is approximately 0.622 or 62.2%.

To calculate the probability that the first two songs played are slow songs, we need to consider the total number of ways the first two songs can be selected and the number of ways to choose two slow songs out of the eight available.

Given:

Total number of songs = 10

Number of slow songs = 8

Step 1: Calculate the total number of ways to choose two songs out of ten (without replacement), which is represented by "10C2" (combinations of 10 things taken 2 at a time):

10C2 = (10 * 9) / (2 * 1) = 45

Step 2: Calculate the number of ways to choose two slow songs out of eight:

8C2 = (8 * 7) / (2 * 1) = 28

Step 3: Find the probability that the first two songs played are slow songs by dividing the number of favorable outcomes (choosing two slow songs) by the total number of possible outcomes (choosing any two songs from the CD):

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 28 / 45 ≈ 0.622

So, the probability that the first two songs played are slow songs is approximately 0.622 or 62.2%.

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Answer: The exact answer is 3.61 weeks, so the "about" answer is 4 weeks.

Step-by-step explanation:

b = $85 + w (10+8)

b = 85 + w (18)

b = 85 + 18w

b is the total amount need in the bank account, so $150.

$150 = $85 + 18w

$150 - $85 = $85 - $85 + 18w

$65 = 18w

$65 / 18 = 18w / 18

3.611 weeks = w

So, it will take about 4 weeks to get $150 in his bank account.

Hope this helps!

Simplify the expression

Put b=150

Answer:

C.

Step-by-step explanation:

-3 7/8 rounds down to -4

4.63 rounds up to 5

-4 x 6 + 5

-24 + 5

-19

her answer (-19.14) also rounds to -19

So yes, it is reasonable and the correct response is C.

Answer:

b) 0.324 < p < 0.416

Step-by-step explanation:

b) 0.324 < p < 0.416

The function f(x) opens upwards, while g(x) opens downwards, and both functions pass through (0, 0), so the correct option is d.

Here we have the two functions:

[tex]f(x) = 2x^2[/tex]

[tex]g(x) = -2x^2[/tex]

Notice tat g(x) = -f(x), which means that g(x) is a reflection across the x-axis of f(x).

The graphs of these functions can be seen below, the one that opens upwards is f(x), the one that opens downwards is g(x).

Then we can conclude that the true statement is:

"f opens upward; g opens downward; both pass through (0, 0)"

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Answer: radius

Step-by-step explanation:

     The radius is the distance halfway across a circle. Since C is the center of the circle and E is along the outside, the answer is;

                       Radius

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill &\$14500\\ P=\textit{initial amount}\dotfill &\$22500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &6\\ \end{cases}[/tex]

[tex]14500=22500(1 - \frac{r}{100})^{6}\implies \cfrac{14500}{22500}=\left( \cfrac{100-r}{100} \right)^6\implies \cfrac{29}{45}=\left( \cfrac{100-r}{100} \right)^6 \\\\\\ \sqrt[6]{\cfrac{29}{45}}=\cfrac{100-r}{100}\implies 100\sqrt[6]{\cfrac{29}{45}}=100-r \\\\\\ r=100-100\sqrt[6]{\cfrac{29}{45}}\implies r\approx \stackrel{\%}{7.06}[/tex]

Using it's concept, it is found that the probability that a person consumes 1,500 to 2,000 calories in a day is given by:

D. 0.50

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Researching the problem on the internet, it is found that out of 500 people, 250 consume 1,500 to 2,000 calories in a day, hence the probability is given by:

p = 250/500 = 0.5.

Which means that option D is correct.

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Answer:

total cost =$ 16 +$ 4.56=$ 20.56

change received = $25 - $ 20.56 = $4.44 .

Step-by-step explanation:

therefore your answer is 4,44 hope this helps

The number 5 is closest to the mean of the distribution, option (B) is correct.

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

From the histogram:

2, 6, 4, 2, 0, 1, 6, 4, 2, 1

The sum of the above data = 28

= 2×1+6×2+4×3+2×4+0×5+1×6+6×7+4×8+2×9+1×10

= 2+12+12+8+6+42+32+18+10

= 142

Mean = 142/28

= 5.07

Thus, the number 5 is closest to the mean of the distribution option (B) is correct.

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Answer:4

Step-by-step explanation:jus done this question

The area of the triangle ABC with the coordinates A(6,0) B(1,5) C(2,0) is 10 square units

The coordinates are given as:

A(6,0) B(1,5) C(2,0) D(4,2)

The area of the triangle is calculated using:

Area = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|

Using the above formula, we have:

Area = 0.5 * |6 * (5 - 0) + 1 * (0 - 0) + 2 * (0 - 5)|

Evaluate the sum of products

Area = 0.5 * |20|

Remove the absolute bracket

Area = 0.5 * 20

Evaluate the product

Area = 10

Hence, the area of the triangle ABC is 10 square units

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Answer:

Area = 996 in^2

Step-by-step explanation:

First, look at the triangle on top, well, like half of it. You can use Pythagorean theorem to find the missing side. See image. Double it to find the base of the whole triangle. Use Area of a triangle:

= 1/2 b•h

to find the area of the top (the triangle).

The 24, used for the triangle base is also the side length of the square below. See image.

Area of a square is:

Area = s^2

OR, just l×w or b×h,

all the same.

Add together the triangle area and the square's area for the final answer. See image.

Step-by-step explanation:

I'm not sure if I got the correct answer since English is not my first language

Answer:

[tex]0 \leqslant x \leqslant 20[/tex]

Answer:

every public company is listed company true or false every public company is listed company true or false every public company is listed company true or false every public company is listed company true or false every public company is listed company true or false every public company is listed company true or false every public company is listed company true or false

Answer:

0.08684 m²

Step-by-step explanation:

1 m = 100 cm

1 m² = (100 cm)²

1 m² = 10000 cm²

868.4 cm² × (1 m²)/(10000 cm²) = 0.08684 m²

Answer:

x = 10

Step-by-step explanation:

I assume you mean

sqrt(x + 6) = x - 6

let's square the whole equation :

x + 6 = (x - 6)² = x² - 12x + 36

x² - 13x + 30 = 0

the general solution to a quadratic equation is

x = (-b ±sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -13

c = 30

x = (13 ±sqrt(13² - 4×1×30))/(2×1) =

= (13 ±sqrt(169 - 120))/2 = (13 ±sqrt(49))/2 =

= (13 ± 7)/2

x1 = (13 + 7)/2 = 20/2 = 10

x2 = (13 - 7)/2 = 6/2 = 3

for x = 10 we get for the original equation

sqrt(10+6) = 10-6 = 4

sqrt(16) = 4

4 = 4

so, x = 10 is a valid solution.

for x = 3 we get

sqrt(3 + 6) = 3 - 6 = -3

sqrt(9) = -3

3 = -3

so, this (x = 3) counts as an invalid solution, because most teachers nowadays expect the square root symbol operation to deliver only the positive solution.

although a square root is actually representing both : the positive AND the negative solution, because the negative number multiplied by itself is the same result as the positive number multiplied by itself.

so, actually

sqrt(9) = -3

± 3 = -3

is still correct and valid. but not what your teacher expects most likely.

in my younger days only the square root of a negative number counted as invalid operation (in the space of Real numbers, of course), and therefore only a solution leading to a square root of a negative number was an invalid solution.

Answer:  855 I think :)

Answer:

1. 6.75x or (6.75, 1)

2.  buys 9 sandwiches.

Step-by-step explanation:

hope this helps if not let me know have a blessed day

Step-by-step explanation:

on the coordinate grid you can imagine a right-angled triangle.

the direct distance between the 2 points is the Hypotenuse (the baseline opposite of the 90° angle).

and the x-coordinate difference and the y- coordinate difference of the 2 points are the 2 legs.

we can then use Pythagoras

c² = a² + b²

with c being the Hypotenuse, a and b being the legs.

so,

distance² = (8-0)² + (2-0)² = 64 + 4 = 68

distance (= length ab) = sqrt(68) = sqrt(4×17) = 2×sqrt(17) =

= 8.246211251...

TheThe line that the rectangle could be rotated around is: C. the vertical line of symmetry.

Analysis

Volume=Base area×height

If the rectangle rotated around horizontal line of symmetry

V1=Ah=πr²h

=π×9×10

=90π

If the rectangle rotated around short line

V2=Ah=πr²h

=π×10²×6

=π×100×6

=600π

If the rectangle rotated around vertical line of symmetry

V3=Ah=πr²h

=π×5²×6

=π×25×6

=150π

Therefore the correct option is C.

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Answer:

here you go..............

Given the ODE

(x - 1) y'' + y' = 0

we assume a solution of the form

[tex]y(x) = \displaystyle \sum_{n=0}^\infty c_n x^n[/tex]

with derivatives

[tex]y'(x) = \displaystyle \sum_{n=0}^\infty n c_n x^{n-1} = \sum_{n=0}^\infty (n+1) c_{n+1} x^n[/tex]

[tex]y''(x) = \displaystyle \sum_{n=0}^\infty (n+1) n c_{n+1} x^{n-1} = \sum_{n=0}^\infty (n+2)(n+1) c_{n+2} x^n[/tex]

Substituting these series into ODE gives

[tex]\displaystyle (x - 1) \sum_{n=0}^\infty (n+2)(n+1) c_{n+2} x^n + \sum_{n=0}^\infty (n+1) c_{n+1} x^n = 0[/tex]

[tex]\displaystyle \sum_{n=0}^\infty (n+2)(n+1) c_{n+2} x^{n+1} - \sum_{n=0}^\infty (n+2)(n+1) c_{n+2} x^n + \sum_{n=0}^\infty (n+1) c_{n+1} x^n = 0[/tex]

[tex]\displaystyle \sum_{n=1}^\infty (n+1)n c_{n+1} x^n - \sum_{n=0}^\infty (n+2)(n+1) c_{n+2} x^n + \sum_{n=0}^\infty (n+1) c_{n+1} x^n = 0[/tex]

[tex]\displaystyle \sum_{n=1}^\infty \bigg((n+1)n c_{n+1} - (n+2)(n+1) c_{n+2} + (n+1) c_{n+1}\bigg) x^n - 2c_2 + c_1 = 0[/tex]

[tex]\displaystyle \sum_{n=1}^\infty \bigg((n+1)^2 c_{n+1} - (n+2)(n+1) c_{n+2}\bigg) x^n - 2c_2 + c_1 = 0[/tex]

[tex]\displaystyle \sum_{n=0}^\infty \bigg((n+1)^2 c_{n+1} - (n+2)(n+1) c_{n+2}\bigg) x^n = 0[/tex]

Then the coefficients [tex]c_n[/tex] are given recursively by

[tex](n+1)^2 c_{n+1} - (n+2)(n+1) c_{n+2} = 0[/tex]

for all n ≥ 0, or equivalently,

[tex]c_{n+2} = \dfrac{n+1}{n+2} c_{n+1}[/tex]

which most closely resembles the second choice.

Answer:

C) x ≥ 11 or x ≤ -3

Explanation:

Given following: |x − 4| ≥ 7

Apply absolute rule: If |u| ≥ 0 then u ≤ -a, u ≥ a

Solving stepwise:

⇒ x - 4  ≤ -7, x - 4 ≥ 7

change sides

⇒ x ≤ -7 + 4, x ≥ 7 + 4

add/subtract integers

⇒ x ≤ -3, x ≥ 11

Answer:

x ≥ 11 or x ≤ -3

Step-by-step explanation:

Hi there! Please take a look at the following explanation and let me know in comment if you have any questions!

[tex]\displaystyle \large{|x-4|\geq 7}[/tex]

To solve an absolute inequality, consider the following theorems.

For b ≥ 0:

(1) If |x-a| ≥ b then we have x-a ≥ b or x-a ≤ -b so that we end up with x ≥ b+a, x ≤ -b+a

(2) If |x-a| ≤ b then we have -b ≤ x-a ≤ b which can be simplified to -b+a ≤ x ≤ b+a

From the inequality, we use the (1) theorem.

[tex]\displaystyle \large{x-4\geq 7, x-4\leq -7}\\\\\displaystyle \large{x\geq 7+4, x\leq -7+4}\\\\\displaystyle \large{x\geq 11, x \leq -3}[/tex]

Therefore, the answer is x ≥ 11 or x ≤ -3