Matt brought $40.50 to the art supply store. He bought a brush, a sketchbook, and a paint set. The brush was 1 6 as much as the sketchbook, and the sketchbook cost 3 4 the cost of the paint set. Matt had $3.00 left over after buying these items.

is simply changing from percentage form to a decimal form usually, but the fractional form works the same.  Check the picture below.

Answer:

98 liters

Step-by-step explanation:

add 39 and 59

Answer:

-9/4, -13/6,-2.1,-26/13

Answer:

-26/13, -13/6,  -2.1, -9/4

Step-by-step explanation:

Sorry its from greatest to least

Answer:

Step-by-step explanation:

Volume of a rectangular prism=length x width x height

450=43*12*x

x=0.87209cm

Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)

The formulas for the area of a regular polygon and the area of a circle given their radii are:

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Therefore, the area of the regular pentagon is:

\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)

The area of the circumcircle is:

\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)

                                                 \(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

Answer:

I have solved it and attached in the explanation.

Step-by-step explanation:

The unit rate of lime is 0.25 dollars.

Limes are on sale.

The sale price is 8 limes for 2 dollars.

The unit rate of lime can be calculated as follows:

A rate is a ratio that compares quantities in different units.

A unit rate is a rate where the second quantity is one unit, such as $80 per pound, 25 km per hour, 80 naira per Ghana cedi's, etc.

Therefore,

8 limes = 2 dollars

1  lime = ?

cross multiply

Hence,

unit rate = 2 × 1 / 8

unit rate = 2 / 8

unit rate = 1 / 4

unit rate of lime = 0.25

Therefore, the unit rate of lime is 0.25 dollars.

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Answer:

8(2m+5)

Step-by-step explanation:

GCF: 8

Factor 8 out of 16 and 40 giving you 2 and 5

DON'T FORGET TO CARRY THE M

Answer:

The correlation is most likely a causation

Step-by-step explanation:

Causation

A change in one variable causes a change in another variable

Coincidence

The two variables are not related at all, but correlate by chance.

Lurking variable

A variable that is not measured in the study (i.e. it's a third variable that is neither the explanatory nor the response variable)

As fertilizer directly affects plant growth, then the correlation is most likely a causation

The DJ will charge them $575.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given that,

Booking fee for DJ = $350

Rate for an hour = $45

Let x be the number of hours DJ is lasting.

Expression to find the total charge for x hours is 350 + 45x.

The Martins want to book the DJ for a party that will last 5 hours.

Cost for the DJ party for Martins = 350 + (45 × 5) = $575

Hence the cost for the DJ party booked by Martins is $575.

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The ratio of number of girls and boys in a class of 30 students is 7:8

The ratio of number of girls and boys if 5 new boys admit in the class.

Let the number of students be x.

According to the question,

7x + 8x = 30

or, 15x = 30

or, x = \( \large {\tt {\frac{30}{15}}} \)

or, x = 2

7x = 7(2) = 14

8x = 8(2) = 16

There were 14 boys and 16 girls in the school.

After admitting 5 new boys, we get

14 + 5 = 19

The ratio of number of girls and boys now is 16:19.

16:19

\(\bold{\huge{\green{\underline{ Solution}}}}\)

\(\bold{\underline{ Given :- }}\)

\(\bold{\underline{ To \: Find :- }}\)

\(\bold{\underline{ Let's \: Begin :- }}\)

In the given right angled triangle, we have

Now, By using trigonometric ratios

\(\bold{\pink{ Sin Φ = }}{\bold{\pink{\frac{Perpendicular }{Hypotenuse}}}}\)

\(\bold{\red{ Cos Φ = }}{\bold{\red{\frac{Base}{Hypotenuse }}}}\)

\(\bold{\blue { tan Φ = }}{\bold{\blue{\frac{Perpendicular }{Base }}}}\)

According to the question :-

\(\bold{ Cos \: 45° = }{\bold{\frac{2}{m}}}\)

\(\bold{ 1/√2= }{\bold{\frac{2}{m}}}\)

\(\bold{\red{ m = 2√2 \: units }}\)

Therefore,

Let the unknown angle be x

\(\sf{ 45° + x + 90° = 180° }\)

\(\sf{ x = 180° - 135 ° }\)

\(\sf{ x = 45° }\)

Now,

\(\bold{ Cos \: x° = }{\bold{\frac{n}{2√2}}}\)

\(\bold{ Cos \: 45° = }{\bold{\frac{n}{2√2}}}\)

\(\bold{ 1/√2= }{\bold{\frac{n}{2√2}}}\)

\(\bold { n = 2√2/√2 }\)

\(\bold{\red{ n = 2\: units }}\)

Thus, The value of m = 2√2 and n = 2

\(\sf{\blue{ Hence, \: option \: D \: is \: Correct }}\)

Answer:

15.4

Step-by-step explanation:

15.39 is closer to 15.40 or 15.4 then 15.30. Thus, the answer here is 15.4.

By answering the presented question, we may conclude that She spends equation 40% of her time at work and 15% of her time on other hobbies. She spends 20% of her time napping.

In mathematics, an equation is an assertion that affirms the equivalence of two factors. An algebraic equation (=) separates two sides of an equation. For instance, the assertion  \("2x + 3 = 9"\) states that the word  \("2x + 3"\) Corresponds to the number "9".

The goal of solution solving is to figure out which variable(s) must still be adjusted for the equations to be true. It is possible to have simple or intricate equations, recurring or complex equations, and equations with one or more components.

For example, in the equations \("x2 + 2x - 3 = 0\)  ," the variable x is lifted to the powercell. Lines are utilized in many areas of mathematics, include algebra, arithmetic, and geometry.

Abby, according to the picture, spent:

She spends 25% of her time in school.

She spends 40% of her time at work and 15% of her time on other hobbies.

Therefore, Furthermore, she spends  \(20\) of her time napping.

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linearity and relevant range include the use of cost behavior pattern data.

the existence of a chain of thoughts or actions wherein one directly follows another: True autobiographies rarely have a linear structure. We don't have a linear existence. Constantly thrown off balance is the narrative's traditional linearity.

The accounting phrase "relevant range" refers to the production or activity parameters that a company must adhere to in order to keep its fixed costs constant. Fixed costs in accounting are constant and unaffected by particular production rates.

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Answer:

No

Step-by-step explanation:

There is no formula

There is no formula

Answer:

(x) ∠CAB

Step-by-step explanation:

In ΔCOD and ΔBOA

\(\frac{OA}{OB} = \frac{OD}{OC} \\\\\implies \frac{OC}{OB} = \frac{OD}{OA}\)

Also,

∠COD = ∠BOA (vertically opposite angles)

⇒ ΔCOD and ΔBOA are similar

⇒ ∠CDO = ∠BAO

⇒ ∠CDB = ∠BAC

⇒ ∠CDB = ∠CAB

The equation formed after the transformations is given as follows:

\(g(x) = \frac{1}{6}\sqrt{x + 3}\)

The parent function in this problem is defined as follows:

\(f(x) = \sqrt{x}\)

For the vertical shrink by a factor of 1/6, the function is multiplied by 1/6, hence it is given as follows:

\(g(x) = \frac{1}{6}\sqrt{x}\)

For the translation left 3 units, we have that x -> x + 3, hence:

\(g(x) = \frac{1}{6}\sqrt{x + 3}\)

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Answer (7, -3)

Step-by-step explanation

Y-axis changes sign of x-coordinate

Answer:

C

Step-by-step explanation:

Oleg is correct because the least common denominator of both is 4, so each must have 4 peices

The value of AB is,

⇒ AB = 5.9

(rounded to nearest tenth)

We have to given that,

A right triangle ABC is shown.

Now, By trigonometry formula,

we get;

⇒ cos 33° = Base / Hypotenuse

Substitute all the values, we get;

⇒ cos 33° = AB / 7

⇒ 0.84 = AB / 7

⇒ AB = 0.84 × 7

⇒ AB = 5.88

⇒ AB = 5.9

(rounded to nearest tenth)

Thus, We get;

AB = 5.9

(rounded to nearest tenth)

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Answer:

y = 3x² + 30x + 27

Step-by-step explanation:

Formula: Ax + By = C

y = 3 (x + 9) (x + 1)

y = 3x + 27x + 3x + 7

y = 3x² + 30x + 27

Because a percent change is based on a comparison of the change in value the starting value and if the starting values are different, then the percent change is different.

When you increase from 45 to 75, you're comparing the change in value (30) to where you started (45).

When you decrease from 75 to 45, you're comparing the same amount of change (30) to a different starting value (75).

30/45 ≠ 30/75

Answer:2, 7, 7, 6

Step-by-step explanation:

Answer:

1) 8/4 = 2

2) 21/3 = 7

3) 56/8 = 7

4) 48/8 = 6

Step-by-step explanation:

To convert a fraction into a whole number: Divide the numerator by the denominator.

What's a numerator?:

A numerator is the part of a fraction above the line. So, 8 in 8/4 is the numerator.

What's a denominator?:

A denominator is the  bottom number in a fraction. So, 4 in 8/4 is the denominator.

1) 8/4 = 8 divided by 4 = 2.

2) 21/3 = 21 divided by 3 = 7

3)56/ 8 = 56 divided by 8 = 7

4) 48 / 8 = 48 divided by 8 = 6

Answer:

Yeah, you're right!

Step-by-step explanation:

For 1/6 it's 17%, so just divide by two and you get 8% (rounded).

Answer:

thats right 8%

Step-by-step explanation:

numbers of samples = 6×2 = 12

6 for a cube , and 2 for a fair coin

numbers of event (5, H) is 1

so, the probability is 1/12 = 1/12 × 100%

= 8.33% => rounded => 8%

Answer:

Step-by-step explanation:

Answer:

15.01

Step-by-step explanation:

10.95+4.06

Answer:

15.01

Hope that helps :-)