simplfy the expression and combine like terms 4 (x - 2) + 2 (x + 1)

Answer:

first blank is "rhombus"

second blank is "rectangle"

third blank is "are congruent"

Step-by-step explanation:

Answer: 10 ft

Step-by-step explanation:

Her desk is a rectangle

Perimeter of a rectangle: 2 ( l + b )

l = 3 ft

b = 2 ft

2 ( 3 + 2 ) = 2 (5) = 10

The perimeter of her desk is 10 ft.

Answer:

x=9

Step-by-step explanation:

So first subtract 8 on both Sides

3x+8-8=35-8

3x=27

Now divide 3 on both sides to isolate the variable x

x=9

So x=9

Answer:

so to do this you need to subtract 8 from 35 to get 27 now do 27 divide by 3 to get 9

3x+8=35

3x=35 - 8 = 27

3x = 27

3x divided by 27 = 9

Step-by-step explanation:

Answer:

The car will travel  525 miles on 15 gallons of gas.

Step-by-step explanation:

Given that car can travel 35 miles using 1 Gallon of gas.

so

Unit rate = 35 miles per gallon

Thus,

The number of miles a car can travel in 15 gallons = 15 × 35

                                                                                    = 525 miles

Thus, the car will travel  525 miles on 15 gallons of gas.

Answer:

70°

Step-by-step explanation:

180-105=75

35+75=110

180-110=70

Step-by-step explanation:

(3•2)+(3•2)+(6.5•3)+(6.5•3)+(2•6.5)+(2•6.5)

=77

Answer:

Step-by-step explanation:

I’m not sure if this is super accurate, but since P is prime, the only factors it has is 1 and itself, meaning that the square root of it will be irrational

Answer:

3 + 14 + 8

Step-by-step explanation:

7a=21

a=21

The equation of the parabola that goes through the three points is:

y = 3x² + 14x + 8

The points are given as:

(-5,13), (0,8), (2,48)

To find the equation of the parabola that goes through the given three points (-5,13), (0,8), and (2,48) using quadratic regression, we need to fit a quadratic equation of the form y = ax² + bx + c to these data points.

Using the three points, we can set up a system of equations:

13 = a(-5)² + b(-5) + c

8 = a(0)² + b(0) + c

48 = a(2)² + b(2) + c

Simplifying these equations, we have:

25a - 5b + c = 13

c = 8

4a + 2b + c = 48

Solving this system of equations, we find that a = 3 and b = 14, and c = 8.

Therefore, the equation of the parabola that goes through the three points is:

y = 3x² + 14x + 8

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Answer:

a)£21.80

b) 3 trips

Step-by-step explanation:

The cost of an adult is $10.

A child’s ticket is $6.

FAMILY DISCOUNT CARD

- 45% off all adults tickets

- Children save 2/5 off of full price tickets

a) How much will it cost to buy 2 adult tickets and children’s tickets?

(a)

Adults: 2 × £10 = £20

(45 ÷ 100) x £20 = £9

£20 - £9 = £11

Children: 3 × £6 = £18

2 /5 of £18 = £7.20

£18 - £7.20 = £10.80

Total: £11 + £10.80 = £21.80

b) The cost of a family discount card is $40 per year. How many times in the same year would 2 adults and 3 children need to go before you start to savemoney on the cost of the card?

(b) Cost without discount = £20 + £18 = £38b)

No card

1 trip

1 × £38 = £38

2 × £38 = £76

3 × £ 38 = £114

With card

£40 + (1 × £21.80) = £61.80

2 trips 2 × £38 = £76 £40 + (2 × £21.80) = £83.60

3 trips 3 x £38 = £114 £40 + (3 × £21.80) = £105.40

3 trips before the discount card starts being cheaper than regular price

9514 1404 393

Answer:

  7800 units per year

Step-by-step explanation:

The increase over 5 years is ...

  89,000 -50,000 = 39,000 . . . . units

Then the increase per year is ...

  (39,000 units)/(5 years) = 7,800 units/year

Answer:

Step-by-step explanation:

Unit rate = 128 ÷ 16 = 8$

Answer:

$8 if it's wrong i'm sorry.

Answer:

the quotient of a number (any letter of the alphabet) n(-5) = nx5 = 7

Step-by-step explanation:

Answer:

A) standard deviation of the sampling distribution of x is 0.5307

B) the sample size needs to be 16, if you want the standard deviation of   the sampling distribution of x to be 0.325

Step-by-step explanation:

Given that;

Population mean μ = 53.7

standard deviation σ = 1.3

sample size n = 6

Sampling distribution of x" follows Normal distribution

x" η N ( μ_x" =μ, σ_x"= σ/√n)

A)

standard deviation of the sampling distribution of x

⇒X" = σ_x" = σ/√n

we substitute

= 1.3/√6

= 1.3 / 2.4494

= 0.5307

Therefore standard deviation of the sampling distribution of x is 0.5307

B)

if σ_x" = 0.325

⇒  σ/√n = 0.325

we substitute in the value of σ

⇒ 1.3/√n = 0.325

√n = 1.3 / 0.325

√n = 4

n = 4²

n = 16

Therefore the sample size needs to be 16, if you want the standard deviation of   the sampling distribution of x to be 0.325

Answer: C.156

Step-by-step explanation:

Given: Total seashells = 160

mean = 120

population standard deviation = 26 grams

The probability that the seashells weigh at least 68 grams :-'

[tex]P(X\geq68) =P(\dfrac{x-\mu}{\sigma}\geq\dfrac{68-120}{26})\\\\=P(z\geq-2)\\\\=P(z<2)\ \ \ [P(Z\geq-z)=P(Z<z)]\\\\= 0.9772\ \ \ [\text{By p-value table}][/tex]

Total seashells weigh at least 68 grams = 0.9772 x 160 = 156.352≈ 156

Hence, the correct option is C.156

Answer:

156/C

Step-by-step explanation:

#platolivesmatter

[tex]\boxed{\boxed{\pink{\sf \leadsto Hence \ the \ area \ of \ shaded \ region \ is 264 cm^2}}}[/tex]

Here , two circles are given which are concentric. The radius of larger circle is 10cm and that of smaller circle is 4cm . And we need to find thelarea of shaded region.

From the figure it's clear that the area of shaded region will be the difference of areas of two circles.

Let the,

[tex]\bf \implies Area_{Shaded}= Area_{bigger}-Area_{smaller} \\\\\bf\implies Area_{Shaded} = \pi R^2 - \pi r^2 \\\\\bf\implies Area_{shaded} = \pi ( R^2-r^2) \\\\\bf\implies Area_{shaded} = \pi [ (10cm)^2 - (4cm)^2] \\\\\bf\implies Area_{shaded} = \pi [ 100cm^2-16cm^2] \\\\\bf\implies Area_{shaded} = \pi \times 84cm^2 \\\\\bf\implies Area_{shaded} = \dfrac{22}{7}\times 84cm^2 \\\\\bf\implies \boxed{\red{\bf Area_{shaded} = 264 cm^2 }}[/tex]

Answer:

2.4 seconds

Step-by-step explanation:

It is given that,

The time for one swing is proportional to the square root of the length of the string.

[tex]T\propto \sqrt{L}[/tex]

or

[tex]\dfrac{T_1}{T_2}=\sqrt{\dfrac{L_1}{L_2}}[/tex] ....(1)

We have,

L₁ = 64 cm, T₁ = 1.6 s, L₂ = 144 cm, T₂ = ?

Substitute all the values in formula (1).

[tex]T_2=\dfrac{T_1}{\sqrt{\dfrac{L_1}{L_2}}}\\\\T_2=\dfrac{1.6}{\sqrt{\dfrac{64}{144}}}\\\\T_2=2.4\ s[/tex]

So, the new time period of the simple pendulum is 2.4 seconds.

Answer:

144 inches squared

Answer:

h = 231 feet

Step-by-step explanation:

Given that,

A person standing 248 feet from the base of a church, x = 248 feet

The angle of elevation to the church's steeple to be 43°.

We need to find the tall of the church. Let the length of the church is h. Using trigonometry to find it.

[tex]\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{h}{x}\\\\h=x\tan\theta\\\\h=248\times \tan(43)\\\\=231.26\ \text{feet}[/tex]

or

h = 231 feet

So, the height of the church is 231 feet.

Answer:

18%

Step-by-step explanation:

Divide 64/303.

Divide 9/303.

Subtract the answers and you'll get 18%.

The percentage of the sample population with brown eyes and black hair is larger than the percentage of the sample population with blue eyes and black hair by 18.25%

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"

Given here, according to the survey, the population with Brown eyes & black hair and Blue eyes and black hair  is 64 and 9 respectively

Also, the marginal total is equal to 303

therefore, the percentages of the two groups are

Brown eyes & black hair =64/303 × 100

                                         = 21.12%

similarly we can calculate  Blue eyes and black hair = 9/303 × 100

                                                                                      = 2.97%

Hence the difference is  21.22% - 2.97% =  18.25% (approx)

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Answer:

n= 37 -8n

the first n is the end result, the second in the equation is the __ number, the nth number

Step-by-step explanation:

Answer: I think it's (0.857142857143 as a fraction equals 857142857143/1000000000000)

Step-by-step explanation:

0.857142857143 as a fraction is 7.714285714287/9, which cannot be simplified further.

Decimals are numbers that have two components, a whole number component and a fractional component, which are separated by a decimal point.

To convert 0.857142857143 to a fraction:

Let x = 0.857142857143

Then 10x = 8.57142857143

Subtracting x from 10x gives:

10x - x = 8.57142857143 - 0.857142857143

Simplifying:

9x = 7.714285714287

Dividing by 9:

x = 0.857142857143 = 7.714285714287/9

Therefore, 0.857142857143 as a fraction is 7.714285714287/9, which cannot be simplified further.

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Answer:

0.99186 probability that the person will not die in the next year, and the correct option is A.

Step-by-step explanation:

Dying and not dying in that year are complementary events, that is, one of them will happen. This means that the sum of their probabilities is 100% = 1.

The probability of dying is:

[tex]p = \frac{814}{100000} = 0.00814[/tex]

So the probability of not dying is given by:

[tex]P = 1-0.00814 = 0.99186[/tex]

0.99186 probability that the person will not die in the next year, and the correct option is A.

Answer:

Average: 4

Standard Deviation: 0

Step-by-step explanation:

Because we don't know how each student did we are going to assume that they all got 20% of the questions right

20% of 20 is 4

Which means that we can assume each student got 4 questions correct

Because all entries are the same the standard deviation is 0

Answer:

yes that is correct...

Step-by-step explanation:

Answer:

1) 4/15

2) 15/15?

Step-by-step explanation:

1) 3/5-1/3

  9/15-5/15

  4/15

2) 15/15?

Answer:

1. [tex]\frac{C}{D}[/tex] = 3.143

2. Circumference

3. Area of the circle is 3850 [tex]cm^{2}[/tex].

   ii. Circumference of the circle is 220 cm.

Step-by-step explanation:

The area, A, and the circumference, c, of a circle can be determined respectively by:

A = [tex]\pi[/tex][tex]r^{2}[/tex]

C = 2[tex]\pi[/tex]r

where r is the radius of the circle.

1. the ratio of the circumference and diameter, D, of a circle is:

r = [tex]\frac{D}{2}[/tex]

so that,

C = 2[tex]\pi[/tex][tex]\frac{D}{2}[/tex]

C = [tex]\pi[/tex]D

[tex]\frac{C}{D}[/tex] = [tex]\pi[/tex]

   = [tex]\frac{22}{7}[/tex]

   = 3.143

2. The distance around a circular region is known as it's circumference.

3. Given a circle of radius 35 cm, then:

A = [tex]\pi[/tex][tex]r^{2}[/tex]

   = [tex]\frac{22}{7}[/tex] x [tex](35)^{2}[/tex]

   = [tex]\frac{22}{7}[/tex] x 1225

   = 22 x 175

A = 3850

Area of the circle is 3850 [tex]cm^{2}[/tex].

C = 2[tex]\pi[/tex]r

   = 2 x [tex]\frac{22}{7}[/tex] x 35

   = 2 x 22 x 5

   = 220

C = 220 cm

Circumference of the circle is 220 cm.

Answer:

1 - 0.3 (3/10)

2 - 1.1 (11/10)

3 - 2.2 (11/5)

For 3/5 (divide) 1/2, the answer is 1.2

Step-by-step-explanation:

3/5 = 0.6

1/2 = 0.5

0.6 / 0.5 = 1.2