Which of the following choices translates the sentence “the difference of three times a number and 20 is 13”?

Answer:

work is shown and pictured

Answer:

x is 226.154…

Step-by-step explanation:

1) x-14=y+196

x=y+196+14

x=y+210

2)x=14y

3) 14y=y+210 collect like terms together

14y-y=210

13y=210 divide both sides by 13

y=16.154

4)x=y+210 meaning:

x=16.154+210

=226.154

Answer:

(A)CPCTC

Step-by-step explanation:

Issa knows that ΔRED ≅ ΔTAN by the SSS theorem.

If two triangles are congruent, their corresponding parts will always be congruent. In fact, their corresponding angles will be equal.

Therefore, Issa concluded that ∠R ≅ ∠T by the fact that Corresponding Parts of Congruent Triangles are Congruent (CPCTC).

The correct option is A.

Similarly, we can also conclude that:

Answer:

the 95th percentile for the sum of the rounding errors is 21.236

Step-by-step explanation:

Let consider X to be the rounding errors

Then; [tex]X \sim U (a,b)[/tex]

where;

a = -0.5 and b = 0.5

Also;

Since The error on each loss is independently and uniformly distributed

Then;

[tex]\sum X _1 \sim N ( n \mu , n \sigma^2)[/tex]

where;

n = 2000

Mean [tex]\mu = \dfrac{a+b}{2}[/tex]

[tex]\mu = \dfrac{-0.5+0.5}{2}[/tex]

[tex]\mu =0[/tex]

[tex]\sigma^2 = \dfrac{(b-a)^2}{12}[/tex]

[tex]\sigma^2 = \dfrac{(0.5-(-0.5))^2}{12}[/tex]

[tex]\sigma^2 = \dfrac{(0.5+0.5)^2}{12}[/tex]

[tex]\sigma^2 = \dfrac{(1.0)^2}{12}[/tex]

[tex]\sigma^2 = \dfrac{1}{12}[/tex]

Recall:

[tex]\sum X _1 \sim N ( n \mu , n \sigma^2)[/tex]

[tex]n\mu = 2000 \times 0 = 0[/tex]

[tex]n \sigma^2 = 2000 \times \dfrac{1}{12} = \dfrac{2000}{12}[/tex]

For 95th percentile or below

[tex]P(\overline X < 95}) = P(\dfrac{\overline X - \mu }{\sqrt{{n \sigma^2}}}< \dfrac{P_{95}- 0 } {\sqrt{\dfrac{2000}{12}}}) =0.95[/tex]

[tex]P(Z< \dfrac{P_{95} } {\sqrt{\dfrac{2000}{12}}}) = 0.95[/tex]

[tex]P(Z< \dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}}) = 0.95[/tex]

[tex]\dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}} =1- 0.95[/tex]

[tex]\dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}} = 0.05[/tex]

From Normal table; Z >   1.645 = 0.05

[tex]\dfrac{P_{95}\sqrt{12} } {\sqrt{{2000}}} =1.645[/tex]

[tex]{P_{95}\sqrt{12} } = 1.645 \times {\sqrt{{2000}}}[/tex]

[tex]{P_{95} = \dfrac{1.645 \times {\sqrt{{2000}}} }{\sqrt{12} } }[/tex]

[tex]\mathbf{P_{95} = 21.236}[/tex]

the 95th percentile for the sum of the rounding errors is 21.236

Answer:

forty two miles over three gallons

Step-by-step explanation:

2 gallons over 32 miles simplifies to 1 gallon over 16 miles, or 1 gallon per 16 miles. This is not the desired result, so we know the first choice is incorrect.

32 miles over 2 gallons simplifies to 16 miles over 1 gallon, or 16 miles per gallon. Again, this is not the desired result, so we know the second choice is also incorrect.

3 gallons over 42 miles simplifies to 1 gallon over 14 miles, or 1 gallon per 14 miles. While this may look correct, note that 1 gallon per 14 miles and 14 miles per gallon are not the same thing, so we know that the third answer is also incorrect.

By process of elimination, we know that the correct answer must be the last option, but let's still simplify it. 42 miles over 3 gallons simplifies to 14 miles over 1 gallon, or 14 gallons per mile. This is in fact the desired result, so we know that the correct answer is the last option. Hope this helps!

Answer:

b=3.1 cm

Step-by-step explanation:

Both of the longer sides will be equal so you can set up the equation (6.3+6.3)+b=15.7. Simplified you get 12.6+b=15.7, subtracting 12.6 from both sides you get that b=3.1 cm. This can be checked because it is also shorter than 6.3 and works correctly in the perimeter.

The attached picture was omitted from the question.

Answer:

C = 41.88 feet

a = 33.1°

b = 56.9°

Step-by-step explanation:

From the diagram, we have a right angle triangle.

C = hypotenuse

C = sqrt(35^2 + 23^2)

C = sqrt(1225 + 529)

C = sqrt(1754)

C = 41.88 feet

The connecting Angles:

Angle 'a'

Using tan = opposite / Adjacent

Tan a = 23 / 35

tan a = 0.6571428

a = tan^-1 (0.6571428)

a = 33.1°

Angle 'b' :

Sum of angles in a triangle = 180

a + b + 90 = 180

33.1 + b + 90 = 180

b + 123.1 = 180

b = 180 - 123.1

b = 56.9°

Answer:

no solution

Step-by-step explanation:

Left and right sides are equal so no solution

Answer:No solution

Step-by-step explanation: I got it right on the test :)

Answer:

2√6

Step-by-step explanation:

x + y = 6

xy = 3

Square the first equation.

x² + 2xy + y² = 36

Subtract 4xy from both sides.

x² − 2xy + y² = 36 − 4xy

Factor.

(x − y)² = 36 − 4xy

Substitute.

(x − y)² = 36 − 4(3)

(x − y)² = 24

Take square root.

x − y = ±√24

x − y = ±2√6

Take absolute value.

|x − y| = 2√6

Answer:

First one: true        Second one: true

Step-by-step explanation:

First Question: the lines will be parellel even though the shape grows or gets smaller

Second Question: the angle will stay the same even if it grows into a larger or smaller shape.

Answer:

Hello there!

~~~~~~~~~~~~~~~~~~~~~~`

Convert the fraction to a decimal by dividing the numerator by the denominator.

[tex]109 / 50 = 2.18[/tex]

Hope this helped you. Brainliest would be nice!

Answer:

the line of g(x) is steeper and has lower y intercept

Step-by-step explanation:

f(x)=1/4x-1

g(x)=1/2x-2

g(x) is steeper because the slope of gx is greater than f(x)

y intercept of gx=-2 and for f(x)=-1

the y intercept of g(x) is lower than the y intercept of f(x)

The steepness of a function is dependent on its slope.

The true statement is: (c) the line of g(x) is steeper and has lower y intercept

The equations are given as:

[tex]\mathbf{f(x)= \frac 14x-1}[/tex]

[tex]\mathbf{g(x)=\frac12x - 2}[/tex]

A linear function is represented as:

[tex]\mathbf{y = mx + b}[/tex]

Where:

For f(x)

[tex]\mathbf{m_1 = \frac{1}4}\\\mathbf{b = -1}[/tex]

For g(x)

[tex]\mathbf{m_1 = \frac{1}2}\\\mathbf{b = -2}[/tex]

By comparison:

This means that: the line of g(x) is steeper and has lower y intercept

Hence, the true option is: (c)

Read more about steep and intercepts at:

https://brainly.com/question/3309622

Answer: 51,000 ; 111,000

Step-by-step explanation:

The formula to calculate the simple interest is: PRT/100

where,

P = principal = 60,000

R = rate = 8.5%

T = time = 10 years

Simple interest =(60000 × 8.5 × 10)/100

= 5100000/100

= 51,000

Total Amount Paid= Principal + Interest

= 60,000 + 51,000

= 111,000

Answer:

904.32 cm^3

Step-by-step explanation:

The formula for the volume of a sphere is V=4/3πr³. Since r is given, we can plug that in for r. I'm assuming that we are using 3.14 for pi, so when we plug in all the values in the equation we get V = 4/3*3.14*6³, which solves out to 904.32.

Answer:

r= 0.87

Step-by-step explanation:

It has the strongest correlation, which means it is closest to the line.

Answer:

1463 : 5080

Step-by-step explanation:

There are 1463 cherry-flavored jelly beans.

There are 5080 non cherry-flavored jelly beans.

The ratio of cherry-flavored jelly beans to non-flavored jelly beans is:

1463 : 5080

Answer:

Height = 3cm

Volume = 50.27cm^3

Step-by-step explanation:

Well to solve for the height with slant height and radius we can use the Pythagorean Theorem,

Which is [tex]a^2 + b^2 = c^2[/tex].

So we have c and a, so we have to fill those in.

(4)^2 + b^2 = (5)^2

16 + b^2 = 25

-16

b^2 = 9

[tex]\sqrt{b} \sqrt{9}[/tex]

b = 3cm

So to find the volume of a cone we use the following formula [tex]\pi r^2 \frac{h}{3}[/tex].

So we have the radius and height so we just fill those in.

(pi)(4)^2(3)/3

(pi)16(1)

pi*16

About 50.27cm^3

Answer:

( x + 36 ) ( x - 2 ) = 0

Step-by-step explanation:

x^2 + 36x - 2x -72 = 0

x ( x + 36 ) - 2 ( x + 36 ) = 0

( x + 36 ) ( x - 2 ) = 0

Answer:

Volume of a sphere = 4/3πr³

π = 3.14

r = radius which is 3in

Volume = 4/3 × 3.14 × 3²

= 37.68

= 38 cubic inches to the nearest hundredth

Hope this helps

Answer:

38 cubic inches

Step-by-step explanation:

Answer:

3.38/6.21=54.428% (0.54428)

Step-by-step explanation:

biocapacity of grazing land of 0.85 ha/person+biocapacity of forest land of 2.53 ha/person

2.53+0.85=3.38

the percentage of biocapacity from grazing and forest land

3.38/6.21=54.428% (0.54428)

Answer:

8 to the power of 1 over 3 equals 2 to the power of 3 whole to the power of 1 over 3 equals 2 to the power of 3 multiplied by 1 over 3 equals 2

Step-by-step explanation:

Options are below

8 to the power of 1 over 3 equals 4 to the power of 3 whole to the power of 1 over 3 equals 4 to the power of 3 multiplied by 1 over 3 equals 4

8 to the power of 1 over 3 equals 2 to the power of 3 whole to the power of 1 over 3 equals 2 to the power of 3 multiplied by 1 over 3 equals 2

8 to the power of 1 over 3 equals 2 to the power of 4 whole to the power of 1 over 3 equals 2 to the power of 4 multiplied by 1 over 3 equals 16

16 to the power of 1 over 4 equals 8 to the power of 2 whole to the power of 1 over 4 equals 8 to the power of 2 multiplied by 1 over 4 equals 8

Given:

8^1/3

if a power is raised to a power, we simplify it by multiplying the exponents; this will create a whole number exponent

if 8 can be rewritten as a number to the 3rd power.

We have

8 = 2*2*2 = 2³

Therefore,

8^1/3=(2^3)^1/3

=2^3×1/3

=2^3/3

=2^1

=2

Answer:

x =- 3 and y = -7

Step-by-step explanation:

2X-2Y=-8

X=2y + 11

We need to isolate both X and Y in both equations

so

2x-2y=-8

(add 2y to both sides)

2x=-8+ 2y

(divide both sides by 2)

x=-4+y and x=2y+11

because both of these equations are the same we can put them together

4+y=2y+11

(subtract y)

4=y+11

(subtract 11)

-7=y

so y = -7

then to find x you just need to plug in y to one of the equations

x=2(-7) + 11

x= -14 +11

x = -3

Answer:

x = - 19, y = - 15

Step-by-step explanation:

Given the 2 equations

2x - 2y = - 8 → (1)

x = 2y + 11 → (2)

Substitute x = 2y + 11 into (1)

2(2y + 11) - 2y = - 8 ← distribute and simplify left side

4y + 22 - 2y = - 8

2y + 22 = - 8 ( subtract 22 from both sides )

2y = - 30 ( divide both sides by 2 )

y = - 15

Substitute y = - 15 into (2) for corresponding value of x

x = 2(- 15) + 11 = - 30 + 11 = - 19

Solution is x = - 19, y = - 15

Answer:

Step-by-step explanation:

measure of angles of a circle=360

angle ACB=360-82=278 degrees

Answer:

Jen has 5c -23 cards now

Step-by-step explanation:

Matt has c baseballs.

Jen has 9 fewer than 5 times as Matt.

Mathematically, what Jen has will be 5c -9 baseballs

Now, Jen gives Matt 14 cards. This means that she lost 14 of her cards and we are going to subtract.

The number of cards she has now is thus 5c-9-14 = 5c -23 cards

Answer:

5n = 1.75

Step-by-step explanation:

The 2 bars are equal thus lower equals upper, that is

5n = 1.75

Answer:

dose it tell you want angle the arc is at?

Step-by-step explanation:

[tex]\bold{\text{Answer:}\quad \text{Recursive formula:}\ a_n=a_{-1}+2n+5}\\.\qquad \qquad \ \text{Explicit formula:}\ a_n=2n^2+3n-6[/tex]

Step-by-step explanation:

-1 → 8 = +9

8 → 19 = +11

19 → 32 = +13

32 → 47 = + 15

a₁ = -1

d = 2n + 5

Recursive formula is: the previous term plus the difference (d)

                               [tex]\large\boxed{a_n=a_{n-1}+2n+5}[/tex]

Explicit formula is the first term plus the product of d and n-1:

[tex]a_n=a_1+d(n-1)\\a_n=-1+(2n+5)(n-1)\\a_n=-1+2n^2-2n+5n-5\\\large\boxed{a_n=2n^2+3n-6}[/tex]

Answer:

11

Step-by-step explanation:

sub 23 with m

23 - 12 = 11

Answer:

Primary source

Step-by-step explanation:

This is because it says "your" house, it means that you are the one looking and counting at the number of cars.

If this was not said "your", there is a higher chance that it is a secondary source, but in this case, it is a primary source.

Its Primary source

HOPE IT HELPS

Answer:

2 & 4

1 & 3

5 & 7

8 & 6

Vertical angles are formed in a set of intersecting lines. They are two differrent angles that are opposite of eachother but have the same angle.

Angle pairs that are vertical angles in the diagram shown when a transversal intersects two parallel lines are:

<1 and <3

<2 and <4

<5 and <7; and

<8 and <6

Recall:

Angles that are regarded as pairs of vertical angles share the same vertex and are directly opposite each other at the point of intersection of two straight lines.

<1 and <3 are directly opposite each other and share same vertex.

<1 and <3 are therefore are a pair of angles that are vertical angles.

<2 and <4; <5 and <7; and <8 and <6 are all directly opposite each other. They are vertical angles pair.

Therefore, angle pairs that are vertical angles in the diagram shown when a transversal intersects two parallel lines are:

<1 and <3

<2 and <4

<5 and <7; and

<8 and <6

Learn more here:

https://brainly.com/question/2889556