A rectangular block of wood measures 5 inches wide. Over time, the width of the block of wood will shrink by 5%. A builder lets the block of
wood shrink. He wants to use it to fill a gap that measures 3.5 inches wide.
How much does the builder need to cut off the wood block so that it will fit exactly in the gap? Enter the answer in the box.

Answer:

36 inches

Step-by-step explanation:

From the diagram attached,

Applying

s = 2πr∅/360

Where s = lenght of the arc, r = radius of the window, ∅ = angle formed in degree, π = pie.

make r the subject of the equation

r = 360s/2π∅................... Equation 2

From the question,

Given: s = 72 inches, ∅ = 2 radians = 114.6°

Constant: 3.14

Substitute these values into equation 2

r = (360×72)/(114.6×3.14×2)

r = 25920/719.688

r = 36 inches

Answer:

Hello! answer: 6

Step-by-step explanation:

8 × 8 = 64

6 × 6 = 36

64 + 36 = 100

√100 = 10 so therefore a = 6 Hope that helps!

fraction form : 8/25

decimal form : 0.32

Answer:

8/25 or if you have to do decimal form it's 0.32

Step-by-step explanation:

Answer:

53

Step-by-step explanation:

one angle is 37

the triangle means one is 90

a trianlge always = 180 total so

(37+90)-180

=53

Its d because 16/12=1.33 same with 20/15 and 40/30 so its 24x1.33 which is 32 there for d is correct

Answer:

Recursive:

Step-by-step explanation:

Common difference ( d ):   17 - 10 = 7

Recursive Arithmetic:

[tex]a_n = a_{n-1} + d[/tex]

[tex]a_n = a_{n-1} + 7[/tex]

[tex]a_1 = -4[/tex]

Hopefully this helped!

Answer:

x = 2

Step-by-step explanation:

GIVEN :-

TO FIND :-

SOLUTION :-

To find the value of x , lets assume that both the triangles are similar to each other. As they are similar , their sides are proportional to each other i.e. :-

[tex]\frac{KJ}{JL} = \frac{QR}{QS}[/tex]

[tex]=> \frac{3}{x} = \frac{12}{x + 6}[/tex]

[tex]=> 3(x + 6) = 12 \times x[/tex]

[tex]=> 3x + 18 = 12x[/tex]

[tex]=> 12x - 3x = 3x + 18 - 3x[/tex]

[tex]=> 9x = 18[/tex]

[tex]=> \frac{9x}{9} = \frac{18}{9}[/tex]

[tex]=> x = 2[/tex]

Answer:

7/100

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 70 and 100 is 10

Divide both the numerator and denominator by the GCD

70 ÷ 10

100 ÷ 10

Reduced fraction:

7

10

Therefore, 70/100 simplified to lowest terms is 7/10.

[tex]\huge{ \mathcal{  \underline{ Answer} \:  \:  ✓ }}[/tex]

First equation :

Second equation :

Now, the equations are in the form of

where,

[tex] \dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2} [/tex]

therefore the equations would have no solution .

_____________________________

[tex]\mathrm{ \#TeeNForeveR}[/tex]

Answer:

12500

Step-by-step explanation:

4.5 × 48=216.

12500 Plus 216= 12,716

The value of the invested money becomes $103393.20 after 4 years if the interest rate is 4.5% and compounded annually.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+r)^t[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          t = How long the money is deposited or borrowed (in years)

We have in the question:

p = $12,500

r = 4.5% ⇒ 0.045

t = 4 years ⇒ 4×12 ⇒ 48 months

Put the above values in the formula, we get;

[tex]\rm A = 12500(1+0.045)^4^8[/tex]

A = 12500×8.27145

A = $103393.20

Thus, the value of the invested money becomes $103393.20 after 4 years if the interest rate is 4.5% and compounded annually.

Learn more about the compound interest here:

brainly.com/question/26457073

Answer:

A. g=6

Step-by-step explanation:

5g-6=24

5g=30

g=30/5

g=6

Answer:

D, g = -8

Step-by-step explanation:

5 (-8) - 6 => 24

-40 - 6 => 24

-46 is NOT greater than or equal to 24.

Answer:

The true statements are :

A. A random variable is a numerical description of the outcome of a statistical experiment.

B. In most​ applications, discrete random variables represent counted​ data.

C. In most applications, continuous random variables represent measured data.

Step-by-step explanation:

It is true statement that,

A. A random variable is a numerical description of the outcome of a statistical experiment.

B. In most​ applications, discrete random variables represent counted​ data.

C. In most applications, continuous random variables represent measured data.

The false statement is -

D. The expected value of a discrete random variable is equal to the standard deviation of the random variable.

Reason -

The mean value, or expected value, of a discrete random variable X is given by the following equation:

μ = E(x) = ∑ x p(x)

And

The variance of a discrete random variable is given by the following formula:

σ²=∑ (x−μ)² P(x)

And

The square root of the variance, or, in other words, the square root of σ², is the standard deviation of a discrete random variable :

σ = √σ²

Answer:

16/21

Step-by-step explanation:

9+7 / 21

16/21

Answer:

16/21

Step-by-step explanation:

The demoninator is 21

There are 9 pens and 7 shoes.

9+7=16

16/21

You can not simplify 16/21, so that is your final answer.

Answer:

option 1

Step-by-step explanation:

The rate of increasing is the fastest in exponential functions.

Then comes powers and last logarithmic functions.

The order it increases at the fastest rate.

[tex]log < powers < exponential[/tex]

Answer:

4

Step-by-step explanation:

h + h

h=2

2+2

4

Answer:

c

Step-by-step explanation:

Answer:

D, a sentence that includes only one independent clause

Step-by-step explanation:

A compound-complex sentence has two independent clauses, and 1 or more dependent clauses. A compound sentence has two independent clauses, and is connected by a conjunction.

This isn't a math question but idrc

Answer:

Solution given

4x+2=-13

subtract each term by 2

4x+2-2=-13-2

divide both side by 4

4x/4=-15/4

we get

x=-15/4

is a required answer.

Let's solve:

[tex]4x+2=−13[/tex]

Step 1: Subtract 2 from both sides.

[tex]4x+2−2=−13−2 \\ 4x = - 15[/tex]

Step 2: Divide both sides by 4.

[tex] \frac{4x}{4} = \frac{ - 15}{4} [/tex]

Answer:

[tex] \frac{ - 15}{4} [/tex]

Answer:

g(x) = (2x)²

Step-by-step explanation:

Answer:

2x+y=7; 3x+2y=16

X = -2

Y = 11

Answer:

c

Step-by-step explanation:

Answer:

[tex]1.\:2^x=64, x=\boxed{6},\\2.\:x=\left(\frac{2}{3}\right)^3,x=\boxed{\frac{8}{125}}\\3.\:3\cdot (3^4)=3^x, x=\boxed{5}\\4.\:\frac{16}{25}=x^2,x=\boxed{\frac{4}{5}},[/tex]

Step-by-step explanation:

[tex]1.\\\\2^x=64,\\\log 2^x=\log64,\\x\log 2=\log 64,\\x=\frac{\log 64}{\log 2}=\boxed{6}[/tex]

[tex]2.\\x=\left(\frac{2}{5}\right)^3=\frac{2^3}{5^3}=\boxed{\frac{8}{125}}[/tex]

3. This problem incorporates an exponent property.

Exponent property used: [tex]a^b\cdot a^c=a^{(b+c)}[/tex], yielding an answer of [tex]\boxed{5}[/tex]

[tex]4.\\\\\frac{16}{25}=x^2,\\x=\sqrt{\frac{16}{25}}=\frac{\sqrt{16}}{\sqrt{25}}=\boxed{\frac{4}{5}}[/tex]

Answer:

1. 6

2. 8/25

3. 5

4. 4/5

Step-by-step explanation:

Answer:

y = -4

Step-by-step explanation:

When y is directly proportional to x,

= y ∝ x

= y = kx

Finding k

the value of y = -2 when x = 4

-2 = k4

k = -2/4

k = -1/2

. What is the value of y when x = 8

Finding y

y = kx

y = -1/2 × 8

y = -4

Step-by-step explanation:

vol of 1st cuboid,

=lxbxh

=4cm×6cm×1cm

=24cm³

vol of 2nd cuboid

= lxbxh

=6cm×3cm×1cm

=18cm³

vol of figure=18cm³+24cm³

= 42cm³

Volume of Cube = a³

side a = 5 Cm

Volume = 5³ = 125 Cm³

Answer:

125m³

Step-by-step explanation:

GIVEN :-

TO FIND :-

GENERAL FORMULAE TO BE USED IN THIS QUESTION :-

Volume of a cube = a³ (where a = length of each side of a cube)

SOLUTION :-

Volume of the cube = 5³ = 125 m³

Answer:

30 strawberry sundaes.

Step-by-step explanation:

We know there is a total of 70 sundaes.

3 sundaes will be strawberry.

4 sundaes will be choclate.

When you add 3 and 4 together, you get 7. This is your total ratio.

So 3/7 of the sundaes are strawberry.

And 4/7 of sundaes are choclate.

We know there is a total of 70 sundaes.

The total ratio we figured out is 7.

If the total sundaes is 70, and the total ration is 7. Then the total sundaes is 10 times bigger than the ratio.

This means we need to multiply the 3 strawberry sundaes and 4 choclate sundaes by 10.

3*10=30

4*10=40

So there are 30 strawberry sundaes and 40 choclate sundaes.

We need to find the strawberry sundae amount, so the answer is 30.

Hope this helps!

Answer: 4/5

Step-by-step explanation:

Answer:

height = 1/4y

Step-by-step explanation:

V(cylinder) = πr²h

V(cone) = πr²h ÷ 3

V(cyl) = πx²y

V(cone) = π(1/2x)²y which simplifies to be πx²y ÷ 4

πx²y = πx²y ÷ 4

if you divide each side by πx² you get:

y = y/4

height is 1/4y

Answer:

12 sales

Let x represent the number of sales each man had.

For Salesman A, he earns $65 per sale; this is 65x.

For Salesman B, he earns $40 per sale; this is 40x.  We also add to this his weekly salary of $300; this gives us 40x+300.

Since their pay was equal, set the two expressions equal:

65x = 40x+300

Subtract 40x from each side:

65x-40x = 40x+300-40x

25x = 300

Divide both sides by 25:

25x/25 = 300/25

x = 12

Step-by-step explanation:

plz brainlist

Answer:

The other person is correct

Step-by-step explanation:

Answer: 6.8 inches

Step-by-step explanation: