Solve the equation 2x + 10 = 30

Answer:

bonds=22000

stock=4000

Step-by-step explanation:

let b  for bonds , and s for stock

b+s=26000

0.05 b +0.08 s=1420

to solve (by elimination)

1- multiply first equation with 0.05 to eliminate b

0.05 b+0.05 s=1300

0.05b+0.08s=1420

subtract two equations:

0.05b+0.05s-0.05b-0.08s=1300-1420

-0.03s=-120

s=120/0.03=4000

b+s=26000

b=26000-4000=22000

check:0.05(22000)+0.08(4000)=1420

Answer:

$22000

Step-by-step explanation:

x*0.05+(26000-x)*0.08= 1420

0.05x - 0.08x + 2080= 1420

0.03x=2080 -1420

0.03x= 660

x= 660/0.03

x= 22000

$22000 = 5% bonds

$4000 = 8% stocks

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:

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:

only the inverse is a function

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:

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:

[tex]\boxed{Area = 3.14 ft^2}[/tex]

Step-by-step explanation:

Radius = r = 2 feet

Angle = θ = π/2 (In radians) = 1.57 radians

Area of Sector = [tex]\frac{1}{2} r^2 \theta[/tex]

Area = [tex]\frac{1}{2} (4)(1.57)[/tex]

Area = 2 * 1.57

Area = 3.14 ft²

Answer:

               [tex]\bold{2\pi\ ft^2\approx6,28\ ft^2}[/tex]

Step-by-step explanation:

360°:2 = 180° so the area of a sector bounded by a 180° arc is a half of area of a circle of the same radius.

[tex]A=\frac12\pi R^2=\frac12\pi\cdot2^2=\frac12\pi\cdot4=2\pi\ ft^2\approx2\cdot3,14=6,28\ ft^2[/tex]

Answer:

Answer:

3x + 3y = 0

7x - y = 8

Step-by-step explanation:

Answer:

320793

Step-by-step explanation:

320793 / 11 = 29163

[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:

work is shown and pictured

Answer:

[tex] x = 5.1 yd [/tex]

Step-by-step Explanation:

Angle of depression is congruent to angle of elevation.

Therefore, angle of elevation of the given figure, which is opposite to x is 25°.

Adjacent length = 11 yd

Opposite length = x

Trigonometric ratio formula for finding x is shown below:

[tex] tan(25) = \frac{opposite}{adjacent} [/tex]

[tex] tan(25) = \frac{x}{11} [/tex]

Multiply both sides by 11 to solve for x

[tex] 11*tan(25) = x [/tex]

[tex] 5.129 = x [/tex]

[tex] x = 5.1 yd [/tex] (to the nearest tenth)

Answer and Step-by-step explanation:

According to the situation, The probabilities for each one is given below:

As there are 20 families

So the probabilities for each one is

For four families have one child is

[tex]= \frac{4}{20}\\\\ = \frac{1}{5}[/tex]

For eight families have two children is

[tex]= \frac{8}{20}\\\\ = \frac{2}{5}[/tex]

For five families have three children is

[tex]= \frac{5}{20}\\\\ = \frac{1}{4}[/tex]

For two families have four children is

[tex]= \frac{2}{20}\\\\ = \frac{1}{10}[/tex]

For one family have five children is

[tex]= \frac{1}{20}[/tex]

Answer:

(Factor out 2x from the expression)

2x (x +3)

Answer:

1:3

Step-by-step explanation:

Please study the diagram briefly to understand the concept.

First, we determine the height of the isosceles trapezoid using Pythagoras theorem.

[tex]4^2=2^2+h^2\\h^2=16-4\\h^2=12\\h=\sqrt{12}\\ h=2\sqrt{3}$ units[/tex]

The two parallel sides of the trapezoid are 8 Inits and 4 units respectively.

Area of a trapezoid [tex]=\dfrac12 (a+b)h[/tex]

Area of the trapezoid

[tex]=\dfrac12 (8+4)*2\sqrt{3}\\=12\sqrt{3}$ Square Units[/tex]

For an equilateral triangle of side length s.

Area  [tex]=\dfrac{\sqrt{3}}{4}s^2[/tex]

Side Length of the smaller triangle, s= 4 Units

Therefore:

Area of the smaller triangle

[tex]=\dfrac{\sqrt{3}}{4}*4^2\\=4\sqrt{3}$ Square units[/tex]

Therefore, the ratio of the area of the smaller triangle to the area of the trapezoid

[tex]=4\sqrt{3}:12\sqrt{3}\\$Divide both sides by 4\sqrt{3}\\=1:3[/tex]

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:

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.

Answer: 20km/h

Step-by-step explanation:

20km/h.  Simply average 15 and 25 by doing (15+25)/2

Hope it helps <3

Answer:

1)2205little cherries

2)0.5.

Step-by-step explanation:

1)7little=2big

?=630big

7×630=2205little cherries

2

2)²/5x=¹/10what is the value of 10x-2

first find the value of x that is ¹/10÷²/5=¼

so x is ¼

insert the value ie 10×¼-2

=2.5-2

=0.5

Answer:

Step-by-step explanation:

y = {9, 10, 11}

x = {2, 3, 4 , 5}

Maximum value of x +  y = 11 + 5 = 16

Minimum value of  y -x = 9 - 2 = 7

[tex]\frac{x+y}{y-x}=\frac{16}{7}[/tex]

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:

The answer is given below

Step-by-step explanation:

a) What is the probability that a randomly selected pregnancy lasts less than 242 days

First we have to calculate the z score. The z score is used to determine the measure of standard deviation by which the raw score is above or below the mean. It is given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Given that Mean (μ) = 247 and standard deviation (σ) = 16 days. For x < 242 days,

[tex]z=\frac{x-\mu}{\sigma}=\frac{242-247}{16}=-0.31[/tex]

From the normal distribution table, P(x < 242) = P(z < -0.3125) = 0.3783

(b) Suppose a random sample of 17 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.

If a sample of 17 pregnancies is obtained, the new mean [tex]\mu_x=\mu=247,[/tex] the new standard deviation: [tex]\sigma_x=\sigma/\sqrt{n} =16/\sqrt{17} =3.88[/tex]

c) What is the probability that a random sample of 17 pregnancies has a mean gestation period of 242 days or less

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{242-247}{16/\sqrt{17} }=-1.29[/tex]

From the normal distribution table, P(x < 242) = P(z < -1.29) = 0.0985

d) What is the probability that a random sample of 49 pregnancies has a mean gestation period of 242 days or less?

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{242-247}{16/\sqrt{49} }=-2.19[/tex]

From the normal distribution table, P(x < 242) = P(z < -2.19) = 0.0143

(e) What might you conclude if a random sample of 49 pregnancies resulted in a mean gestation period of 242 days or less?

It would be unusual if it came from mean of 247 days

f) What is the probability a random sample of size 2020 will have a mean gestation period within 11 days of the mean

For x = 236 days

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{236-247}{16/\sqrt{20} }=-3.07[/tex]

For x = 258 days

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{258-247}{16/\sqrt{20} }=3.07[/tex]

From the normal distribution table, P(236 < x < 258) = P(-3.07 < z < 3.07) = P(z < 3.07) - P(z < -3.07) =0.9985 - 0.0011 = 0.9939

Answer:

Add each given variable

(6x + 10) + (x + 2) + x = 8x + 12

The sum of all the angles equals 180ᴼ

8x + 12 = 180

Subtract 12 from both sides

8x = 168

Divide by 8 on both sides

x = 21

Now plug in 21 for each x to find the measure of each angle.

(6[21] + 10) = 126 + 10 = 136ᴼ

(21 + 2) = 23ᴼ

x = 21ᴼ

Answer:

11

Step-by-step explanation:

sub 23 with m

23 - 12 = 11

Answer:

dose it tell you want angle the arc is at?

Step-by-step explanation:

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

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:

We can prove that ΔTMB ≅ ΔTMD and ΔTMA ≅ ΔTMC by ASA. This means that BM = MD = BD / 2 = 8.5 and that AM = CM = 5 which means that CD = MD - CM = 8.5 - 5 = 3.5.

Answer:

Translate 3 units to the left

Step-by-step explanation:

Answer:

Choice 3

Step-by-step explanation:

A(-5,-1) and B(4, 1)

Distance AB is calculated as x²+y², where x= 4-(-5)=9 and y= 1-(-1)=2

Point P is at 1/4 of distance from point A, so its coordinates will be at 1/4 of full distance from A to B in term of both coordinates:

So P= (-11/4, -1/2) and choice 3