please help Find: ∠x ∠a ∠b

Answer:

Hi! Answer will be below.

Step-by-step explanation:

The answer is 450.

If you divide 1.8 and 0.004 the answer you should get is 450.

Below I attached a picture of how to do long division...the picture is an example.

Hope this helps!:)

⭐️Have a wonderful day!⭐️

Answer:

The fraction that this is true for = 7/13

Step-by-step explanation:

From the above question

Let the numerator be represented by a

Let the denominator be represented by b

If you add 5 to both the numerator and the denominator of a fraction, you obtain 2/3

This means:

a + 5/b + 5 = 2/3

Cross Multiply

3(a + 5) = 2(b + 5)

3a + 15 = 2b + 10

Collect like terms

3a - 2b = 10 - 15

3a - 2b = -5..........Equation 1

If you subtract 5 from both the numerator and the denominator of the same fraction, you obtain 1/4

This means:

a - 5/b - 5 = 1/4

Cross Multiply

4(a - 5) = 1(b - 5)

4a - 20 = b - 5

Collect like terms

4a - b = 20 - 5

4a - b = 15..........Equation 2

b = 4a - 15

3a - 2b = -5..........Equation 1

4a - b = 15..........Equation 2

Substitute 4a - 15 for b in equation 1

3a - 2b = -5..........Equation 1

3a - 2(4a - 15) = -5

3a - 8a + 30 = -5

Collect like terms

3a - 8a = -5 - 30

-5a = -35

a = -35/-5

a = 7

Therefore, the numerator of the fraction = 7

Substitute 7 for a in Equation 2

4a - b = 15..........Equation 2

4 × 7 - b = 15

28 - b =15

28 - 15 = b

b = 13

The denominator = b is 13.

Therefore,the fraction which this is true for = 7/13

To confirm

a) If you add 5 to both the numerator and the denominator of a fraction, you obtain 2/3

This means:

a + 5/b + 5 = 2/3

7 + 5/ 13 + 5 = 2/3

12/18 = 2/3

Divide numerator and denominator by of the left hand side by 6

12÷ 6/ 18 ÷ 6 = 2/3

2/3 =2/3

If you subtract 5 from both the numerator and the denominator of the same fraction, you obtain 1/4

This means:

a - 5/b - 5 = 1/4

7 - 5/13 - 5 = 1/4

2/8 = 1/4

Divide the numerator and denominator of the left hand side by 2

2÷2/8 ÷ 2 = 1/4

1/4 = 1/4

From the above confirmation, the fraction that this is true for is 7/13

Answer:

see details below

Step-by-step explanation:

The price of a boat that Arthur wants is $29,450. Arthur finances this by paying $6000 down and monthly payment of $792.22 for 36 months.

a. Determine the amount to be financed.​​​​​​​15a. ___$23450____________

29450 - 6000 = 23450

b. Determine the installment price.​​​​​​​​b. ___$792,22______________

"monthly payment of $792.22"

c. Determine the finance charge.​​​​​​​​c. __$5069.92_______________

A = 792.22

n = 36

finance charge = total paid - amount to be financed

= 36*792.22 - 23450

= 5069.92

Answer:

15) 2.08m

Step-by-step explanation:

We kow tanA= p/b

Here, A=33°

b=3.2m

Then,

tan33°=p/3.2

0.65=p/3.2

p=0.65*3.2

p=2.08

So, The height of tree is 2.08m

14) 59.58ft

tan50°=p/b

1.19=p/50

p=59.58ft

So, The height of signpost is 59.58ft

In both of these problems, we will be using trigonometry! Remember, SOH-CAH-TOA.

14. x = 13.5950 ft

Visualization of the problem is attached below.

We want to find out the opposite side to the angle, and we know the adjacent side. Therefore, we should use the tangent function.

tan(50) = x / 50

x = tan(50) * 50

x = 13.5950 ft (round off wherever you need)

15. x = 241.0016 m

The visualization of the problem is already given. We know the same information as we need in the previous problems, an angle and an adjacent side, and we want to find the opposite side. Therefore, we should use the tangent function.

tan(33) = x / 3.2

x = tan(33) * 3.2

x = 241.0016 (round off wherever you need)

Hope this helps!! :)

Answer:

I NEED POINTS

Step-by-step explanation:

Answer: 3/50

Step-by-step explanation:

0.06 = 6/100 , 100 would be the denominator because we have two figures after the decimal point. Each figures can also be represented by 10,

Again,

0.06 = 6 × 10-²

Now 0.06 = 6/100

= 3/50.

Therefore, the fractional form = 3/50 in its lowest term.

Answer:

Step-by-step explanation:

area = base x height

where base = 20 ft.

        height = ?

           area = 120 ft²

plugin values into the formula

120 = 20 x height

height = 120  

               20

height = 6 ft.

Answer: 1 30/39

Step-by-step explanation:

Because y/x=z and y/z=x are true with the same values, simply do 7 2/3 divided by 4 1/3 to get 69/39.

Hope it helps <3

Answer:

Step-by-step explanation:

its 5

1/6 *2 *3 *5=

1/3*3*5=

5

Answer:

x ≥ 4

Step-by-step explanation:

Well to find the inequality we need to single out x,

4x - 1 ≥ 15

+1 to both sides

4x ≥ 16

Divide 4 by both sides

x ≥ 4

Thus,

x is greater than or equal to 4.

Hope this helps :)

Answer:

calls first evening = 26

calls second evening  = 80

calls third evening = 20

Step-by-step explanation:

Let x = calls third evening

x+6 = calls first evening

4x = calls second evening

x+6 + 4x + x = total calls = 126

Combine like terms

6x+6 = 126

Subtract 6 from each side

6x =120

Divide by 6

6x/6 =120/6

x = 20

x+6 = calls first evening = 20+6 = 26

4x = calls second evening = 4*20 = 80

Let x = calls third evening = 20

Answer:

8 units

Step-by-step explanation:

We need to rewrite an equation in the standard for  a circle form.

r is radius.

(x−h)²+(y−k)²= r²

x² + y² – 2x + 8y – 47= 0

x² - 2x + y² + 8y - 47 = 0

x² - 2*x *1+ 1 ²- 1² + y² + 2*4*y + 4² - 4² - 47 = 0

(x - 1)² + (y + 4)² - 1 - 16 -47 =0

(x - 1)² + (y + 4)² - 64=0

(x - 1)² + (y + 4)² = 8²

Radius is 8.

The radius of the circle is 8 units

The radius of a circle is a line drawn from the center to the circumference of the circle

The equation of the circle is given as;

[tex]x^2 + y^2 - 2x + 8y - 47 = 0[/tex]

Rewrite the equation as:

[tex]x^2 - 2x + y^2 + 8y = 47[/tex]

Next, we rewrite the equation in the standard form

So, we have:

x^2 - 2x + 1^2 - 1^2 + y^2 + 8y + 4^2 - 4^2 = 47

Evaluate the exponents

x^2 - 2x + 1 - 1 + y^2 + 8y + 16 - 16 = 47

Rewrite the equation as follows:

x^2 - 2x + 1 + y^2 + 8y + 16 = 47 + 1 + 16

Express as perfect squares

(x - 1)² + (y + 4)² = 64

(x - 1)² + (y + 4)² = 8^2

The radius of the circle is calculated as:

r^2 = 8^2

By comparison, we have:

r = 8

Hence, the radius of the circle is 8 units

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Answer:

C.I =  0.7608   ≤ p ≤   0.8392

Step-by-step explanation:

Given that:

Let consider a  random sample n = 400 candidates where  320 residents indicated that they voted for Obama

probability [tex]\hat p = \dfrac{320}{400}[/tex]

= 0.8

Level of significance ∝ = 100 -95%

= 5%

= 0.05

The objective is to  develop a 95% confidence interval estimate for the proportion of all Boston residents who voted for Obama.

The confidence internal can be computed as:

[tex]=\hat p \pm Z_{\alpha/2} \sqrt{\dfrac{ p(1-p)}{n } }[/tex]

where;

[tex]Z_{0.05/2}[/tex] = [tex]Z_{0.025}[/tex] = 1.960

SO;

[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.8(1-0.8)}{400 } }[/tex]

[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.8(0.2)}{400 } }[/tex]

[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.16}{400 } }[/tex]

[tex]=0.8 \pm 1.960 \sqrt{4 \times 10^{-4}}[/tex]

[tex]=0.8 \pm 1.960 \times 0.02}[/tex]

[tex]=0.8 \pm 0.0392[/tex]

= 0.8 - 0.0392     OR   0.8 + 0.0392  

= 0.7608    OR    0.8392

Thus; C.I =  0.7608   ≤ p ≤   0.8392

Hey there! I'm happy to help!

We see that the father is 60 years old, and the son is half of that age, so this means that the son is 30 years old.

We want to see the age the son was at when the father was four times his age. We know that the father is thirty years older than him, so we can write this equation with s representing the age of the son.

s+30=4s   (30 years older than the son is equal to to four times the son's age at the time)

We subtract 30 from both sides.

s=4s-30

We subtract 4s from both sides.

-3s=-30

We divide both sides by -3.

s=10

Therefore, the boy was 10 when his father was four times his age. This is because his father would have been 40 because that is 30 more years than 10, and it is four times ten!

Have a wonderful day! :D

Answer:

C. 1/8

Step-by-step explanation:

Probability of shooting a goal on a throw is 2/4 = 1/2.

Probability of 3 in a row is (1/2)³ = 1/8.

Answer:

2(x^2 + 8x -55)

Step-by-step explanation:

Well to do the box method we first need to simplify the given equation further to,

[tex]2x^2 + 16x - 110\\[/tex],

For this quadratic the box method doesn't work so we can divide everything by 2 make make it

2(x^2 + 8x -55)

Thus,

[tex]2x^2 + 16x - 110\\[/tex] factored is 2(x^2 + 8x -55).

Hope this helps :)

Answer:

The meadian decreases by 1.5 when the outlier is removed.

Step-by-step explanation:

Well first we need to find the median of the following data set,

(75, 63, 58, 59, 63, 62, 56, 59)

So we order the set from least to greatest,

56, 58, 59, 59, 62, 63, 63, 75

Then we cross all the side numbers,

Which gets us 59 and 62.

59 + 62 = 121.

121 / 2 = 60.5

So 65 is the median before the outlier is removed.

Now when we remove the outlier which is 75.

Then we order it again,

56, 58, 59, 59, 62, 63, 63

Which gets us 59 as the median.

Thus,

the median height decreases by 1.5 units when the outlier is removed.

Hope this helps :)

Answer:

Step-by-step explanation:

Given two lines y=(3a+2)x-2 and 2y=(a-4)x+2, Since both lines are parallel to each other, this means that the slope of both lines are the same

Let's get the slope of both equation. For the first equation;

y=(3a+2)x-2

We can see that the equation is written in this form y = mx+c where m is the slope of the line. On comparison, the slope of the given line is 3a+2

Similarly for the second line;

2y=(a-4)x+2

Re-writing in the standard format we will have;

y = (a-4)x/2+2/2

y = (a-4)x/2 + 1

The slope of the second line is (a-4)/2

On equating the slope of both lines to get the value of 'a' we will have;

3a+2 = (a-4)/2

Cross multiplying

2(3a+2) = a-4

6a+4 = a-4

Collecting like terms;

6a-a = -4-4

5a = -8

a = -8/5

Hence the value of a is -8/5

Answer:

y= 250( 1-0.21)^x

Step-by-step explanation:

This represents exponential decay

The equation represents a population of 250 animals that decreases at an annual rate of 21% will be p = 250(0.79)[tex].^t[/tex] The correct option is C.

The mathematical expression f(x)=[tex]e^t[/tex] denotes the exponential function. The term typically refers to the positive-valued function of a real variable, unless otherwise specified.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

It is given that a population of 250 animals is decreasing at an annual rate of 21%.

p = a x b[tex].^t[/tex]

p = a x (1+r)[tex].^t[/tex]

p = 250 x (1+(-0.21))[tex].^t[/tex]

p = 250(0.79)[tex].^t[/tex]

Note that r = -0.21 is negative to indicate we have exponential decay.

Hence, the equation represents a population of 250 animals that decreases at an annual rate of 21% will be p = 250(0.79)[tex].^t[/tex] The correct option is C.

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Answer:

Step-by-step explanation:

Simplify each term.

y ≤ −2x/5 + 2

Find the slope and the y-intercept for the boundary line.

Slope: -2/5

Y-intercept: 2

Graph a solid line, then shade the area below the boundary line since

y is less than -2x/5 + 2

y ≤ −2x/5 + 2

Hope this can help

Answer:

Option D is correct.

Angle C = 70°

Step-by-step explanation:

The sum of angles in a triangle = 180°

So,

(Angle A) + (Angle B) + (Angle C) = 180°

(Angle A) = 67°

(Angle B) = 43°

(Angle C) = ?

67° + 43° + (Angle C) = 180°

Angle C = 180 - 67 - 43 = 70°

Angle C = 70°

Hope this Helps!!!

Answer:   90°

Step-by-step explanation:

As known ∡EGC=(arcEC+arcDF)/2

arcEC+arcDF=70°*2

5x+10+11x+2=140

16x+12=140

16x=128

x=128:16

x=8

So arcDF=11*x+2=11*8+2=90°

The measure of arc DF is 90°.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

Given,  Circle A with chords EF and CD that intersect at point G,

arc EC = 5x + 10°

arc DF = 11x + 2°

∠EGC = 70°

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite

so

∠EGC=(1/2)[arc EC+arc DF]

substitute the values

70 = 1/2(5x + 10 + 11x + 2)

70 = 1/2(16x + 12)

140 = 16x + 12

16x = 128

x = 128/16 = 8

so ac DF = 11x + 2

arc DF = 11(8) + 2

arc DF= 88 + 2 = 90°

Hence the value of arc DF is 90°.

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Answer:

A:-4

Step-by-step explanation:

If you simplify 9(2x+1)<9x-18 you will get 9x<-27. That will mean x<-3 and the only answer for something less than -3 is -4.

If the answer was right, please put 5 stars.

Answer:

The answer would be-4

Step-by-step explanation:

Here,

9(2x+1) < 9x-18

or, 18x+9 < 9x-18

or, 18x-9x<-18-9

or, 9x<-27

or, x= -27/9

Therefore, the value of x is -4.

Hope it helps...

Answer:

19

Step-by-step explanation:

7 supersricpt 8

Answer:

(16x + 21) and (16x - 6)

Step-by-step explanation:

f(g(x)) = f(6 + 4x)

Applying the f(x) function on (6 + 4x) gives

4(6 + 4x) - 3

Which equals 16x + 24 - 3

= 16x + 21

g(f(x)) = g(4x - 3)

Applying the g(x) function on (4x - 3) gives

6 + 4(4x - 3)

Which equals 6 + 16x - 12

= 16x - 6

Answer:

(g∘f)(x)=48x2+48x+10

(g∘f)(x)=12x^2-6

Step-by-step explanation:

To find (f∘g)(x), use the definition of (f∘g)(x),

(f∘g)(x)=f(g(x))

Substituting 3x2−2 for g(x) gives

(f∘g)(x)=f(3x2−2)

Find f(3x2−2), where f(x)=4x+2, and simplify to get

(f∘g)(x)(f∘g)(x)(f∘g)(x)=4(3x2−2)+2=12x2−8+2=12x2−6

To find (g∘f)(x), use the definition of (g∘f)(x),

(g∘f)(x)=g(f(x))

Substituting 4x+2 for f(x) gives

(g∘f)(x)=g(4x+2)

Find g(4x+2), where g(x)=3x2−2, and simplify to get

(g∘f)(x)=3(4x+2)^2−2

(g∘f)(x)=48x2+48x+12−2

(g∘f)(x)=48x2+48x+10

Answer:

1. [tex]H_{0}[/tex] : p = 0.70 , [tex]H_{a}[/tex] : p > 0.70

2. Test Statistic : 0.54 , P value : 0.2946

3. Fail to reject null Hypothesis

4. No.

Step-by-step explanation:

1. Null hypothesis is 70% of children receive antibiotics.

Alternative hypothesis is more than 70% of children receive antibiotics.

2. Test statistic is calculated as;

z = [tex]\frac{p (1 - p)}{\sqrt{\frac{p (1-p}{n} )} }[/tex]

z = [tex]\frac{0.01}{0.0185}[/tex]

z = 0.54

3. p value is calculated as;

1 - right tailed probability

1 - 0.7054 = 0.2946

Answer:

Step-by-step explanation:

In ACB and ECD

AC =~ CE [ Given ]

BC =~ CD [ Given ]

<ACD =~ <ECD [ Vertical angles ]

Hence, ∆ ACB =~ ECD by SAS congruency of triangles.

Then, <B = <D

In ∆ABC , sum of all three angles must be 180°

<A + <B + <C = 180°

plug the values

[tex] 30 + < d \: + 70 = 180[/tex]

Add the numbers

[tex]100 + < d = 180[/tex]

Move constant to R.H.S and change it's sign

[tex] < d = 180 - 110[/tex]

Subtract the numbers

[tex] < d = 80[/tex] °

Hope this helps..

Best regards!!

Answer:

1.35

Step-by-step explanation:

next cube above 540 is 729

to get to 729: 729 / 540 = 1.35

n = 1.35

Answer:

Margin of Error = ME =± 5.2592

Step-by-step explanation:

In the given question n= 20 < 30

Then according to the central limit theorem z test will be applied in which the standard error will be  σ/√n.

Sample Mean = μ = 64

Standard Deviation= S= σ = 12

Confidence Interval = 95 %

α= 0.05

Critical Value for two tailed test for ∝= 0.05 = ±1.96

Margin of Error = ME = Standard Error *Critical Value

ME = 12/√20( ±1.96)=

ME    = 2.6833*( ±1.96)= ± 5.2592

The standard error for this test is σ/√n

=12/√20

=2.6833