A restaurant catered a party for 45 people. A child’s dinner (c) cost $15 and an adult’s dinner (a) cost $25. The total cost of the dinner was $1,015. How many children and adults were at the party? Use the table to guess and check.

Number of People
a
c
c + a = 45
15 c + 25 a = 1,015 dollars




9 adults and 36 children
10 adults and 35 children
34 adults and 11 children
36 adults and 9 children

Answer:

48cm²

Step-by-step explanation:

PQ=(24-5-5)/2=7

This means PR is 14 and US is 10.

The height of the parallelogram is base times height, so 28/7=4

Now we just look at it as one big parallelogram.

4(14+10)/2=48 cm²

Answer:

{-3.5, 3.5}

Step-by-step explanation:

Interpreting

|-x| = 3.5

gives

3.5 = +(-x)  or 3.5 = -(-x)

or

x = + / - 3.5

so the answer is

{-3.5, 3.5}

Answer:

A

Step-by-step explanation:

Answer:

We could rewrite 7/2 as 7a + 2

Step-by-step explanation:

Complex numbers is when real numbers [i.e: 1, 1/2, 200, 5/7, etc..) and an imaginary numbers [numbers that give a negative result when squared] are combine together.

Answer:

Step-by-step explanation:

can you at least telllus what is in the drop box

Answer:

i need help this too

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given,

x = 5

Now, let's find the value of C

[tex]c = 3x - 2[/tex]

plug the value of x

[tex] = 3 \times 5 - 2[/tex]

Multiply the numbers

[tex] = 15 - 2[/tex]

Calculate the difference

[tex] = 13[/tex]

Hope this helps..

Best regards!!

Answer:

0.431 inches

Step-by-step explanation:

We were given the following values:

Height the tennis ball was dropped = 100in

Rebound height = 58in

We have to find the rebound ratio

= 58in/100in = 0.58

The formula to be used

Height on nth bounce = Initial height × (Rebound ratio)ⁿ

Where n = number of bounce

Height on the 10th bounce = 100 × (0.58)^10

Height on the 10th bounce = 0.4308042069inches

Approximately, the height on the 10th bounce = 0.431 inches.

Answer:

Lucy needs to invest $55,194.16

Step-by-step explanation:

The given information are;

The interest rate of the account = 7% compounded daily

The amount at the end of 6 years = $84,000

The time duration = 6 years

The amount Lucy

The formula for compound interest is

[tex]A(t) = P \times \left ( 1 + \dfrac{r}{n} \right )^{n \times t}[/tex]

Where;

r = The interest rate = 7% = 0.07

n = The number of times a year = 365

t = The number years = 6 years

A(t) =  The amount after 6 years = $84,000

P = The initial amount invested

Therefore, we have;

[tex]\$ 84,000 = P \times \left ( 1 + \dfrac{0.07}{365} \right )^{365 \times 6}[/tex]

[tex]P = \dfrac{\$84,000}{\left ( 1 + \dfrac{0.07}{365} \right )^{365 \times 6}} =\dfrac{\$84,000}{1.522} = \$55,194.16[/tex]

Therefore, Lucy needs to invest $55,194.16.

Answer:

[tex]\sf x=\frac{1}{10}[/tex]

Step-by-step explanation:

Rewrite expression with bases of 4.

[tex]\sf{4^{\frac{3}{4} }} \times \sf({4^\frac{1}{2} )^x =(4^2)^{\frac{2}{5} }[/tex]

Apply law of exponents, when bases are same for exponents in multiplication, add the exponents. When a base with an exponent has a whole exponent, then multiply the two exponents.

[tex]\sf{4^{\frac{3}{4} }} \times \sf{4^{\frac{1}{2} x}=4^{\frac{4}{5} }[/tex]

[tex]\sf{4^{\frac{3}{4} +\frac{1}{2} x}=4^{\frac{4}{5} }[/tex]

Cancel same bases.

[tex]\sf \frac{3}{4} +\frac{1}{2} x=\frac{4}{5}[/tex]

Subtract 3/4 from both sides.

[tex]\sf \frac{1}{2} x=\frac{1}{20}[/tex]

Multiply both sides by 2.

[tex]\sf x=\frac{1}{10}[/tex]

Step-by-step explanation:

2^{2*3/4} × 2^{x}=2^{4×2/5}

2^{3/2} × 2^{x}= 2^{8/5}

2^{3/2+x}=2^{8/5}

equate powers

{3+2x}/2= 2^2

5{3+2x}= 2{8}

15+10x=16

collect like terms

10x=16-15

10x=1

divide both sides by 10

x=1/10

x=0.1

Answer:

7

Step-by-step explanation:

i Hope this helps

Answer:

Step-by-step explanation:

[tex] {(5 - 6)}^{2} \times (4 + 3)[/tex]

Calculate the difference

[tex] = {( - 1)}^{2} \times (4 + 3)[/tex]

Add the numbers

[tex] = {( - 1)}^{2} \times 7[/tex]

Evaluate the power

[tex] = 1 \times 7[/tex]

Any expression multiplied by 1 remains the same

[tex] = 7[/tex]

Hope this helps...

Best regards!!

Answer:

[tex]7 < x < 37[/tex] -- Triangle 1

[tex]6.5 < x < 19.9[/tex] -- Triangle 2

[tex]22 < x < 46[/tex] -- Triangle 3

[tex]21 < x < 67[/tex] -- Triangle 4

Step-by-Step Explanation:

Given

2 sides of a triangle

1. 22 and 15

2. 13.2 and 6.7

3. 34 and 12

4. 23 and 44

Required

Determine the range of the third side in the above triangles

Represent the third side with x

We'll make use of the following conditions to calculate  the range of the third side;

[tex]22 + x > 15[/tex]

[tex]22 + 15 > x[/tex]

[tex]15 + x > 22[/tex]

Solving

[tex]22 + x > 15[/tex]

Make x the subject of formula

[tex]x > 15 - 22[/tex]

[tex]x > -7[/tex]

Solving

[tex]22 + 15 > x[/tex]

[tex]37 > x[/tex]

Solving

[tex]15 + x > 22[/tex]

Make x the subject of formula

[tex]x > 22 - 15[/tex]

[tex]x > 7[/tex]

The next step is to dismiss the inequality with negative digit; So, we're left with

[tex]37 > x[/tex] and [tex]x > 7[/tex]

Rewrite both inequalities

[tex]x < 37[/tex] and [tex]7 < x[/tex]

Combine the two inequalities

[tex]7 < x < 37[/tex]

Represent the third side with x

We'll make use of the following conditions to calculate  the range of the third side;

[tex]13.2 + x > 6.7[/tex]

[tex]13.2 + 6.7 > x[/tex]

[tex]6.7 + x > 13.2[/tex]

Solving

[tex]13.2 + x > 6.7[/tex]

Make x the subject of formula

[tex]x > 6.7 - 13.2[/tex]

[tex]x > -6.5[/tex]

Solving

[tex]13.2 + 6.7 > x[/tex]

[tex]19.9 > x[/tex]

Solving

[tex]6.7 + x > 13.2[/tex]

Make x the subject of formula

[tex]x > 13.2 - 6.7[/tex]

[tex]x > 6.5[/tex]

The next step is to dismiss the inequality with negative digit; So, we're left with

[tex]19.9 > x[/tex] and [tex]x > 6.5[/tex]

Rewrite both inequalities

[tex]x < 19.9[/tex] and [tex]6.5 < x[/tex]

Combine the two inequalities

[tex]6.5 < x < 19.9[/tex]

Represent the third side with x

We'll make use of the following conditions to calculate  the range of the third side;

[tex]34 + x > 12[/tex]

[tex]34 + 12 > x[/tex]

[tex]12 + x > 34[/tex]

Solving

[tex]34 + x > 12[/tex]

Make x the subject of formula

[tex]x > 12 - 34[/tex]

[tex]x > -22[/tex]

Solving

[tex]34 + 12 > x[/tex]

[tex]46 > x[/tex]

Solving

[tex]12 + x > 34[/tex]

Make x the subject of formula

[tex]x > 34 - 12[/tex]

[tex]x > 22[/tex]

The next step is to dismiss the inequality with negative digit; So, we're left with

[tex]46 > x[/tex] and [tex]x > 22[/tex]

Rewrite both inequalities

[tex]x < 46[/tex] and [tex]22 < x[/tex]

Combine the two inequalities

[tex]22 < x < 46[/tex]

Represent the third side with x

We'll make use of the following conditions to calculate  the range of the third side;

[tex]23 + x > 44[/tex]

[tex]23 + 44 > x[/tex]

[tex]23 + x > 44[/tex]

Solving

[tex]23 + x > 44[/tex]

Make x the subject of formula

[tex]x > 23 - 44[/tex]

[tex]x > -21[/tex]

Solving

[tex]23 + 44 > x[/tex]

[tex]67 > x[/tex]

Solving

[tex]23 + x > 44[/tex]

Make x the subject of formula

[tex]x > 44 - 23[/tex]

[tex]x > 21[/tex]

The next step is to dismiss the inequality with negative digit; So, we're left with

[tex]67 > x[/tex] and [tex]x > 21[/tex]

Rewrite both inequalities

[tex]x < 67[/tex] and [tex]21 < x[/tex]

Combine the two inequalities

[tex]21 < x < 67[/tex]

D. The line is perpendicular to the plane determined by the two lines.

Remember how you get to 3D space?

You take one axis called x and perpendicularly intersect it with y axis and you get a 2D plane. Now take a 2D plane and perpendicularly intersect it with an axis z and you get 3D euclidean space.

Hope this helps.

Answer:

855.298 m^3

Step-by-step explanation:

The volume of a cylinder equation is piR^2H.

So pi5.5^2×9

855.298 m^3

Answer:

A

Step-by-step explanation:

Kenny scored 13 points, and Micheal scored p points.  They scored a total of 27 points.  This means that 27 is the sum of their scores.  The answer is A.

13 + p = 27

Answer:

It’s b or it’s 13+p=27

Step-by-step explanation:

Answer:

             [tex]\bold{A_{_{\Delta XYZ}}=927.5\ cm^2}[/tex]

Step-by-step explanation:

m∠Z = 180° - 118° - 28° = 34°

[tex]\sin(28^o)\approx0.4695\\\\\sin(118^o)=\sin(180^o-62^o)=\sin62^o\approx0.8829 \\\\\sin(34^o)\approx0.5592\\\\[/tex]

[tex]\dfrac{\overline{XY}}{\sin Z}=\dfrac{\overline{YZ}}{\sin X}\\\\\\\overline{XY}=\dfrac{\overline{YZ}}{\sin X}\cdot\sin Z\\\\\\\overline{XY}=\dfrac{42}{0.4695}\cdot0.5592\\\\\overline{XZ}=50.024281...\\\\\\A_{_{\Delta XYZ}}=\frac12\cdot\overline{XY}\cdot\overline{YZ}\cdot\sin(\angle Z)\\\\\\A_{_{\Delta XYZ}}\approx\frac12\cdot50.0243\cdot42\cdot0.8829=927.4955...\approx927.5[/tex]

Answer:

1. True

2. False.

3. True.

Step-by-step explanation:

1. The total area within any continuous probability distribution is equal to 1.00: it is true because the maximum probability (value) is one (1), therefore, the total (maximum) area is also one (1).

Hence, for continuous probability distribution: probability = area.

2. For any continuous probability distribution, the probability, P(x), of any value of the random variable, X, can be computed: False because it has an infinite number of possible values, which can not be counted or uncountable.

Hence, it cannot be computed.

3. For any discrete probability distribution, the probability, P(x), of any value of the random variable, X, can be computed: True because it has a finite number of possible values, which are countable or can be counted.

Hence, it can be computed.

Answer:

Real interest rate = -1%

Step-by-step explanation:

Real interest rate=Nominal interest rate - inflation rate

From the above,

Nominal interest rate=1%

Inflation rate=2%

Real interest rate=Nominal interest rate - inflation rate

=1% - 2%

= -1%

Real interest rate = -1%

Real interest rate shows you what it really costs borrowers to pay back their loans.

if the real interest rate is greater than zero, the amount you pay back is worth more in real terms than the money you borrowed.

if the real interest rate is below zero as in the above case, the amount you will pay back is less worth in real terms than the money you borrowed.

Answer:

0.5645

Step-by-step explanation:

De la pregunta anterior, se nos dan los siguientes valores para el equipo de Ludlow

Probabilidad de jugar de noche = 70% = 0.7

Probabilidad de ganar en la noche = 50% = 0.5

Probabilidad de jugar durante el día = 30% = 0.3

Probabilidad de ganar durante el día = 90% = 0.9

Probabilidad de que cuando ganaron ayer, el juego se jugó por la noche =

(Probabilidad de jugar de noche × Probabilidad de ganar de noche) ÷ [(Probabilidad de jugar de noche × Probabilidad de ganar de noche) + (Probabilidad de jugar de día × Probabilidad de ganar de día)]

Probabilidad de que cuando ganaron ayer, el juego se jugó de noche = (0.5 × 0.7) ÷ (0.5 × 0.7) + (0.9 × 0.3)

= 0.35 ÷ 0.35 + 0.27

= 0.35 ÷ 0.62

= 0.5645

La probabilidad de que el partido se haya jugado de noche = 0.5645

Answer:

a   1 : 5

Step-by-step explanation:

Blue mables: 3

green and red marbles: 8 + 7 = 15

then, the radio blue:(green+red) is:

3 : 15

simplified unit rate is:

3/3 = 1

15/3 = 5

then:

3:15

is equal to:

1:5

Answer:

a   1 : 5

Answer:

30.045

Step-by-step explanation:

the length of rectangle=140 which is also the diameter of circle

R=d/2=140/2=70 ( which is the width of rectangle)

perimeter of rectangle=2l+2w=140+280=420

perimeter of semicircle=πr+d=70π+140=359.911

the difference between two perimeter

(perimeter of rectangle- perimeter of semi circle) =

420-359.911=60.089

since only one shaded area :

60.089/2=30.0445 close to 30.045

Answer:

O B. 17 units

Step-by-step explanation:

The chord is AC and the radius of the circle is perpendicular to the chord at B. AB = 8.5 units. According to the perpendicular bisector theorem, if the radius of a circle is perpendicular to a chord then the radius bisects the chord. This means that chord AC is bisected by the radius of the circle at point B. The length of the circle is calculated using:

[tex]AB=\frac{AC}{2}\\ AC=2*AB\\cross multiplying:\\AC = 2*8.5\ units\\AC = 17 \ units[/tex]

The length of the chord is 17 units.

Answer:

The answer is 17 units :D

Step-by-step explanation:

Answer:

[tex]\approx[/tex] 11 litres of water will fit inside the container.

Step-by-step explanation:

As per the given figure, we have a container formed with combination of a right angled cone placed at the top of a right cylinder.

Given:

Height of cylinder, [tex]h_1[/tex] = 15 cm

Diameter of cylinder/ cone, D = 26 cm

Slant height of cone, l = 20 cm

Here, we need to find the volume of container.[tex]\\Volume_{Container} = Volume_{Cylinder}+Volume_{Cone}\\\Rightarrow Volume_{Container} = \pi r_1^2 h_1+\dfrac{1}{3}\pi r_2^2 h_2[/tex]

Here,

[tex]r_1=r_2 = \dfrac{Diameter}{2} = \dfrac{26}{2} =13\ cm[/tex]

To find the Height of Cylinder, we can use the following formula:

[tex]l^2 = r_2^2+h_2^2\\\Rightarrow h_2^2 = 20^2-13^2\\\Rightarrow h_2^2 = 400-169\\\Rightarrow h_2^2 = 231\\\Rightarrow h_2=15.2\ cm \approx 15\ cm[/tex]

Now, putting the values to find the volume of container:

[tex]Volume_{Container} = \pi \times 13^2 \times 15+\dfrac{1}{3}\pi \times 13^2 \times 15\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 15+\pi \times 13^2 \times 5\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 20\\\Rightarrow Volume_{Container} = 10613.2 \approx 10613\ cm^3[/tex]

Converting [tex]cm^{3 }[/tex] to litres:

[tex]10613 cm^3 = 10.613\ litres \approx 11\ litres[/tex]

[tex]\approx[/tex] 11 litres of water will fit inside the container.

Answer:

<

Step-by-step explanation:

Answer: sample space

Step-by-step explanation: In determining the probability of a certain event occurring or obtaining a particular outcome from a set of different possible outcomes, such as in the toss of coin(s), rolling of fair die(s), the sample space comes in very handy as it provides a simple breakdown and segmentation of all possible events or outcomes such that in Calculating the probability of occurrence of a certain event, the event(s) is/are located in the sample space and the ratio taken over the total number of events.

Answer:

Step-by-step explanation:

If the number of representatives of a multi-level marketing company as a function of the number of days that have passed can be modeled by the exponential function R(d) = 150(1.03)^d, to calculate the number of representatives that the company have after 75 days, we will substitute d = 75 into the modeled equation.

R(75) = 150(1.03)^75

R(75) = 150*9.1789

R(75) = 1,376.835

Hence, the company have about 1377 representatives after 75 days.

Answer:

B

Step-by-step explanation:

common difference is 3

explicit formula is

first term + ( n-1 ) * common difference

= -7 + ( n-1) * 3

Answer:

$35

Step-by-step explanation:

Using the formula provided, d=(p−c)÷2 (where d is the discount, p is the original price, and c is the store's cost for the dress.) we can determine the discount.

The original price is 120,

d=(120−c)÷2

The store's cost is 50,

d=(120−50)÷2

So we subtract 120 and 50 to get

d=(70)÷2

70 divide by two is

d= 35

The discount is $35

Answer:

b) 36 inches

Step-by-step explanation:

Length  of the  wire = Outside circumference of the cylindrical tube * length of the cylinder

= 4 * 9

= 36 inches

Length of the wire will be same to the surface area of the cylinder

Surface area of cylinder = circumference * length

Answer:  b) {-3, 0.5}

Step-by-step explanation:

The new equation is the original equation plus 6.  Move the original graph UP 6 units.  The solutions are where it crosses the x-axis.

[tex]\text{Original equation:}\quad f(x)=\dfrac{15}{x}-\dfrac{9}{x^2}\\\\\\\text{New equation:}\quad\dfrac{15}{x}+6=\dfrac{9}{x^2}\\\\\\.\qquad \qquad f(x)= \dfrac{15}{x}-\dfrac{9}{x^2}+6[/tex]

+6 means it is a transformation UP 6 units.  

Solutions are where it crosses the x-axis.

The curve now crosses the x-axis at x = -3 and x = 0.5.