Ryder is building a workbench.
The top of the workbench is a rectangular piece of plywood that is 6.25 feet long and 1.83 feet wide.

Part A
Round the length and width to the nearest whole number.
Then estimate the perimeter of the workbench.
Which of the following equations models this estimate of the perimeter?
A. 6 + 6 + 2 + 2 = 16
B. 6 × 2 = 12
C. 7 + 7 + 2 + 2 = 18
D. 7 × 2 = 14

Part B
Round the length and width to the nearest tenth.
Then estimate the perimeter of the workbench.
Which of the following equations models this estimate of the perimeter?
A. 6.2 + 6.2 + 1.8 + 1.8 = 16
B. 6.2 × 1.8 = 11.16
C. 6.3 + 6.3 + 1.8 + 1.8 = 16.2
D. 6.3 × 1.8 = 11.34

Answer:

City A and city B will have equal population 25years after 1990

Step-by-step explanation:

Given

Let

[tex]t \to[/tex] years after 1990

[tex]A_t \to[/tex] population function of city A

[tex]B_t \to[/tex] population function of city B

City A

[tex]A_0 = 10000[/tex] ---- initial population (1990)

[tex]r_A =3\%[/tex] --- rate

City B

[tex]B_{10} = \frac{1}{2} * A_{10}[/tex] ----- t = 10 in 2000

[tex]A_{20} = B_{20} * (1 + 20\%)[/tex] ---- t = 20 in 2010

Required

When they will have the same population

Both functions follow exponential function.

So, we have:

[tex]A_t = A_0 * (1 + r_A)^t[/tex]

[tex]B_t = B_0 * (1 + r_B)^t[/tex]

Calculate the population of city A in 2000 (t = 10)

[tex]A_t = A_0 * (1 + r_A)^t[/tex]

[tex]A_{10} = 10000 * (1 + 3\%)^{10}[/tex]

[tex]A_{10} = 10000 * (1 + 0.03)^{10}[/tex]

[tex]A_{10} = 10000 * (1.03)^{10}[/tex]

[tex]A_{10} = 13439.16[/tex]

Calculate the population of city A in 2010 (t = 20)

[tex]A_t = A_0 * (1 + r_A)^t[/tex]

[tex]A_{20} = 10000 * (1 + 3\%)^{20}[/tex]

[tex]A_{20} = 10000 * (1 + 0.03)^{20}[/tex]

[tex]A_{20} = 10000 * (1.03)^{20}[/tex]

[tex]A_{20} = 18061.11[/tex]

From the question, we have:

[tex]B_{10} = \frac{1}{2} * A_{10}[/tex]  and  [tex]A_{20} = B_{20} * (1 + 20\%)[/tex]

[tex]B_{10} = \frac{1}{2} * A_{10}[/tex]

[tex]B_{10} = \frac{1}{2} * 13439.16[/tex]

[tex]B_{10} = 6719.58[/tex]

[tex]A_{20} = B_{20} * (1 + 20\%)[/tex]

[tex]18061.11 = B_{20} * (1 + 20\%)[/tex]

[tex]18061.11 = B_{20} * (1 + 0.20)[/tex]

[tex]18061.11 = B_{20} * (1.20)[/tex]

Solve for B20

[tex]B_{20} = \frac{18061.11}{1.20}[/tex]

[tex]B_{20} = 15050.93[/tex]

[tex]B_{10} = 6719.58[/tex] and [tex]B_{20} = 15050.93[/tex] can be used to determine the function of city B

[tex]B_t = B_0 * (1 + r_B)^t[/tex]

For: [tex]B_{10} = 6719.58[/tex]

We have:

[tex]B_{10} = B_0 * (1 + r_B)^{10}[/tex]

[tex]B_0 * (1 + r_B)^{10} = 6719.58[/tex]

For: [tex]B_{20} = 15050.93[/tex]

We have:

[tex]B_{20} = B_0 * (1 + r_B)^{20}[/tex]

[tex]B_0 * (1 + r_B)^{20} = 15050.93[/tex]

Divide [tex]B_0 * (1 + r_B)^{20} = 15050.93[/tex] by [tex]B_0 * (1 + r_B)^{10} = 6719.58[/tex]

[tex]\frac{B_0 * (1 + r_B)^{20}}{B_0 * (1 + r_B)^{10}} = \frac{15050.93}{6719.58}[/tex]

[tex]\frac{(1 + r_B)^{20}}{(1 + r_B)^{10}} = 2.2399[/tex]

Apply law of indices

[tex](1 + r_B)^{20-10} = 2.2399[/tex]

[tex](1 + r_B)^{10} = 2.2399[/tex] --- (1)

Take 10th root of both sides

[tex]1 + r_B = \sqrt[10]{2.2399}[/tex]

[tex]1 + r_B = 1.08[/tex]

Subtract 1 from both sides

[tex]r_B = 0.08[/tex]

To calculate [tex]B_0[/tex], we have:

[tex]B_0 * (1 + r_B)^{10} = 6719.58[/tex]

Recall that: [tex](1 + r_B)^{10} = 2.2399[/tex]

So:

[tex]B_0 * 2.2399 = 6719.58[/tex]

[tex]B_0 = \frac{6719.58}{2.2399}[/tex]

[tex]B_0 = 3000[/tex]

Hence:

[tex]B_t = B_0 * (1 + r_B)^t[/tex]

[tex]B_t = 3000 * (1 + 0.08)^t[/tex]

[tex]B_t = 3000 * (1.08)^t[/tex]

The question requires that we solve for t when:

[tex]A_t = B_t[/tex]

Where:

[tex]A_t = A_0 * (1 + r_A)^t[/tex]

[tex]A_t = 10000 * (1 + 3\%)^t[/tex]

[tex]A_t = 10000 * (1 + 0.03)^t[/tex]

[tex]A_t = 10000 * (1.03)^t[/tex]

and

[tex]B_t = 3000 * (1.08)^t[/tex]

[tex]A_t = B_t[/tex] becomes

[tex]10000 * (1.03)^t = 3000 * (1.08)^t[/tex]

Divide both sides by 10000

[tex](1.03)^t = 0.3 * (1.08)^t[/tex]

Divide both sides by [tex](1.08)^t[/tex]

[tex](\frac{1.03}{1.08})^t = 0.3[/tex]

[tex](0.9537)^t = 0.3[/tex]

Take natural logarithm of both sides

[tex]\ln(0.9537)^t = \ln(0.3)[/tex]

Rewrite as:

[tex]t\cdot\ln(0.9537) = \ln(0.3)[/tex]

Solve for t

[tex]t = \frac{\ln(0.3)}{ln(0.9537)}[/tex]

[tex]t = 25.397[/tex]

Approximate

[tex]t = 25[/tex]

Answer:1380

Step-by-step explanation: 12x115

Answer:

1,380

Step-by-step explanation: 12 times 115 gives you the product of 1,380. :)

Hope this is helpful

Answer:

Square tables used

Step-by-step explanation:

x represents the number of square tables used since it is being multiplied times 8 which is the number of people a square table can fit

Answer:

answer in pictures

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

135-75 = 60

HOPE IT HELPS

[tex]3 {x}^{2} + 11x - 4[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex](3x - 1)(x + 4) \\ \\ = 3x(x + 4) - 1(x + 4) \\ \\ = 3 {x}^{2} + 12x - x - 4 \\ \\ = 3 {x}^{2} + 11x - 4[/tex]

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

Answer: 6 hours and 10 minutes

Step-by-step explanation:

Answer:

It is 4

Step-by-step explanation:

1 times 1 for square

3 times 3 then divide by 2 = 3

add together

4

Answer:

a = 5.5 in²

Step-by-step explanation:

square

a = lw

a = 1 * 1

a = 1

Triangle

a = (1/2)bh

a = (1/2) * 3 * 3

a = 4.5

combined figure

a = 1 + 4.5

a = 5.5 in²

Answer:

(6290.678 ; 7790.742)

Step-by-step explanation:

Given the data :

5640, 5090, 6590, 6380, 7165, 8440, 9980

The sample mean, xbar = Σx / n = 49285 / 7 = 7040.71

The 90% confidence interval :

Xbar ± Margin of error

Margin of Error = Zcritical * σ/√n

Since the σ is known, we use the z- distribution

Zcritical at 90% confidence = 1.64

Hence,

Margin of Error = 1.64 * 1210/√7

Margin of Error = 750.032

90% confidence interval is :

7040.71 ± 750.032

Lower boundary = 7040.71 - 750.032 = 6290.678

Upper boundary = 7040.71 + 750.032 = 7790.742

(6290.678 ; 7790.742)

Answer:

3 /4

Step-by-step explanation:

The probability that selected person is a female Given she is married :

This is a conditional probability in the form ; A given B

P(A|B) = P(AnB) / P(B)

Let, Female = F ; Married = M

P(F|M) = P(FnM) / P(M) = 150 / 200 = 3 / 4

Answer:

4/9

Step-by-step explanation:

2+16 = 18 total marbles

16 ÷ 2= 8 plastic marbles

Since there are 18 total marbles and 8 plastic red marbles we can say that there is a probability of 8/18.

8/18 in simplest form is 4/9.

Hope this helps! Brainliest?

Answer:

a coin flip

Step-by-step explanation:

The probability of an event is a number describing the chance that the event will happen. An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of zero.

Answer:

20 degree

Step-by-step explanation:

x + x + 70 = 110 degree (sum of two opposite interior angle equal to the exterior angle formed)

2x = 110 - 70

x = 40/2

x = 20 degree

Answer:

[tex]\left[\begin{array}{ccc}3\\3.8\end{array}\right][/tex]

Step-by-step explanation:

Here we want to compute the product of two matrices, one 2x2, and other 2x1.

[tex]\left[\begin{array}{ccc}0.3&0.3\\0.35&0.4\end{array}\right]*\left[\begin{array}{ccc}4\\6\end{array}\right][/tex]

Remember that in the product, we multiply the rows of the first one by the columns of the second one, then the product is just:

[tex]\left[\begin{array}{ccc}0.3&0.3\\0.35&0.4\end{array}\right]*\left[\begin{array}{ccc}4\\6\end{array}\right] = \left[\begin{array}{ccc}0.3*4 + 0.3*6\\0.35*4 + 0.4*6\end{array}\right] = \left[\begin{array}{ccc}3\\3.8\end{array}\right][/tex]

Step-by-step explanation:

kayo na po bahala mag calculate

Answer:

x = 25

Step-by-step explanation:

3x-15 = 2x+10

x-15 = 10

x = 25

Answer:

x = 25 degree

Step-by-step explanation:

3x - 15 = 2x + 10 (their relation will be alternate interior angles if they [tex]l_{1}[/tex] and [tex]l_{2}[/tex] are parallel)

3x - 2x = 10 + 15

x = 25 degree

Answer:

[tex]x^2+y^2+z^2-18x-4y+2z-21=0[/tex]

Step-by-step explanation:

From the question we are told that:

Diameters has endpoints: [tex](-14. -3, -6) & (-4, 7, 4)[/tex]

Generally the equation for Center of The sphere is mathematically given by

 [tex]C=(\frac{-14+(-4)}{2},\frac{-3+(7)}{2},\frac{-6+(4)}{2})[/tex]

 [tex]C=(9,2,-1)[/tex]

Generally the equation for Radius of the sphere is mathematically given by

 [tex]R=\sqrt{(9-2)^2+(2-9)^2+(-1-2)^2}[/tex]

 [tex]R=\sqrt{107}[/tex]

Therefore the Equation of the Sphere is

 [tex](x-9)^2+(y-2)^2+(z+1)^2=107[/tex]

 [tex](x^2-18x+81)+(y^2-4y+4+(z^2+2z+1))=107[/tex]

 [tex]x^2+y^2+z^2-18x-4y+2z-21=0[/tex]

Answer:

VPQ = 83°

Step-by-step explanation:

You can draw a circle around the point P, and a circle have 360°, so it means that the sum off all the angles have ro be 360°. Some of these angles have the same measure, because they're formed by the same lines segments, they are:

SPR = UPV; TPU = RPQ; TPS = VPQ

360 - SPR - UPV - RPQ - TPU = VPQ + TPS

As some of they are equal, we can just multiply they by 2:

360 - 2×SPR - 2×RPQ = 2× VPQ

360 - 2×35 - 2×62 = 2×VPQ

360 - 70 - 124 = 2×VPQ

2 VPQ = 166

VPQ = 166/2

VPQ = 83°

Answer:

ur mom

Step-by-step explanation:

doin doin

Answer:

m∠ACD = 130

Step-by-step explanation:

If ABC is an isosceles, AB = AC and m∠A = 80°, then m∠B and m∠C is equal to 50°.

This is because angles in a triangle adds up to 180°.

180° - 80° = 100°/2 = 50°

∴ m∠ACD = 130°, this is because the interior opposite angles in a triangle is supplementary to the opposite exterior angle:

50° + 80° = 130°

Or

Angles on a straight line adds up to 180°.

180° - 50° = 130°

Answer:

the answer is the alphabet A at the picture

The circle must be on -5 and arrow drawn to the right. Hence the correct answer is number line A

Given the inequality expression

-4(x+3) <= -2-2x

Expand the inequality

-4x - 12 <= -2-2x

Collect the like terms

-4x + 2x <= -2+12

-2x <= 10

Divide both sides by -2

-2x/-2 >= 10/-2

x >= -5

For the number line, the circle must be on -5 and arrow drawn to the right. Hence the correct answer is number line A.

Learn more on inequality expression: https://brainly.com/question/24372553

Answer:

Perimeter of the sector = 2r + length of arc= 2(3.5)+11= 7+11=18 meters exactly the length of the rope.

Step-by-step explanation:

The perimeter of the sector is equivalent to the length of the rope which is 18 meters

Perimeter of the sector= 2 x radius + length of the arc

But length of arc= radius x central angle in radian

18= 2(3.5)+ 3.5(central angle in radians)

18=7+3.5 (central angle in radians)

18–7=3.5(central angle)

11=3.5(central angle)

central angle =11/3.5=3.14 radians or pi radians

Angle in degrees =pi radians x 360 degrees/2pi radians =pi radians x 180 degrees/pi radians = 180 degrees

Therefore the central angle = 180 degrees because pi radians is half of 2pi radians which is half of 360 degrees

Notes: This sector shape is a semicircle because the central angle is 180 degrees

Check: Length of Arc for semicircle =3.5(pi radians)=11 meters

Perimeter of the sector = 2r + length of arc= 2(3.5)+11= 7+11=18 meters exactly the length of the rope.

Answer:

the next three terms, 0.075,0.0375,0.01875 (common ratio 0.5)

the formula is 0.3*0.5^n-1

the formula for finding the nth term of a geometric sequence preset would be

a*r^n-1

a is first term

r is common ratio

Step-by-step explanation:

Answer:

below

Step-by-step explanation:

p = 2( a + b)

p = 2(24 +16)

p =80 in

p semicircle

=πr

= 3.142 *8

= 25.136

p of figure

p =80 +25.136

p=105.136 in

Answer:

0.83333333333

Step-by-step explanation:

One-half plus one-third equals 5/6 or 0.8333.

Given that:

Expression: 1/2 + 1/3

To add one-half (1/2) and one-third (1/3), to find a common denominator and then add the fractions together.

The least common denominator (LCD) of 2 and 3 is 6. To convert the fractions to have a common denominator of 6, multiply the numerator and denominator of 1/2 by 3, and the numerator and denominator of 1/3 by 2:

1/2 × 3/3 = 3/6

1/3 × 2/2 = 2/6

Now that the fractions have a common denominator of 6, add them:

3/6 + 2/6 = 5/6

3/6 + 2/6 = 0.8333

Therefore, one-half plus one-third equals 5/6 or 0.8333.

Learn more about Divisor here:

https://brainly.com/question/30925934

#SPJ6

9514 1404 393

Answer:

  4/10 and 10/25

Step-by-step explanation:

If each of the ratios reduces to the same lowest terms, then they are a proportion. All are in lowest terms except the first pair. Reducing those gives ...

  4/10 = 10/25 = 2/5

4/10 and 10/25 form a proportion

__

All of the other pairs are pairs of different ratios, so do not form a proportion.

Answer:

option A : 25

Step-by-step explanation:

Given :

P = (- 6, 7) , Q = ( 2 , 1 ) , R = ( -1 , -3)

Find the length of PQ ,QR , PR.

Using distance formula to find the lengths.

[tex]distance = \sqrt{(x_2 - x_1 )^2 + (y_ 2- y_1)^2[/tex]

[tex]PQ = \sqrt{(2 -- 6)^2 + (1-7)^2} = \sqrt{8^2 + 6^2 } = \sqrt{64 + 36 } =\sqrt{100} = 10\\\\QR = \sqrt{(2 --1)^2 + (-3-1)^2}= \sqrt{3^2 + 4^2} =\sqrt{9+ 16} =\sqrt{25} = 5\\\\PR = \sqrt{(-1--6)^2 + (-3 -7)^2} = \sqrt{5^2 + 10^2} = \sqrt{25 + 100} = \sqrt{125}[/tex]

Clearly , the triangle satisfies Pythagoras theorem :

Square of larger side = Sum of squares of other sides.

Therefore , PQR is a right triangle,

with base = 5, height 10 and slant height(hypotenuse) = [tex]\sqrt{125}[/tex] .

[tex]Area = \frac{1}{2} \times base \times height[/tex]

       [tex]=\frac{1}{2} \times 5\times 10\\\\= 5 \times 5 \\\\= 25 \ square\ units[/tex]

Answer:

18

Step-by-step explanation:

f(x) = 2x^2

Let x = -3

f(-3) = 2 * (-3)^2

Exponents first

f(-3)=2 *9

f(3) = 18

Answer:

f ( - 3 ) = 18

Step-by-step explanation:

f ( x ) = 2x²

Find f ( - 3)

let , x = - 3

lf ( - 3 ) = 2 ( -3 )²

f ( - 3 ) = 2 × ( - 3 )²

Evaluate the power

f ( -3) = 2 × 9

multiply the numbers

f ( - 3 ) = 18