A baby is 19 inches long at birth. After 14 months, the baby is 30 inches long. What is the rate of change?

Answer:

70° and 110°

Step-by-step explanation:

If two angles forms a linear pair, this means that the sum of the angles is 180°. If the measure of one angle is x and the measure of the other angle is 1.4 times x plus 12∘

Let A be the first angle = x°

Let B be the second angle = (1.4x+12)°

Since they form a linear pair, then

A+B = 180°

x + 1.4x+12 = 180°

2.4x = 180-12

2.4x = 168

x = 168/2.4

x = 70°

The measure of angle A = 70°

The measure if angle B = 1.4x+12

B = 1.4(70)+12

B = 98+12

B = 110°

The measure of both angles are 70° and 110°

Answer:

The answer is 3.

Step-by-step explanation:

This is because f(-3) = -(-3) = 3.

Answer:

3.5

Step-by-step explanation:

I did the test, also, take the people multiply by score, u get 66 total, divided by 19=number of students, is 3.5-ish

The mean for gymnastic score is, 3.5

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

Zahara asked the students of her class their gymnastic scores and recorded the scores in the table shown in table.

Now, We get;

The mean for gymnastic score is,

= ((1×0)+(1×1)+(2×2)+(6×3)+(4×4)+(3×5)+(2×6)) / 19

= 3.47

= 3.5

Thus, The mean for gymnastic score is, 3.5

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Step-by-step explanation:

55 ÷ 11 + (13 x 3)

5 + (13 x 3)

5 + 39

44

Answer:

44

Step-by-step explanation:

13 * 3 = 39

55/11 = 5

5 + 39 = 44

I hope I helped!  Please mark me brainliest!

Answer:

Misty is the more consistent employee

Step-by-step explanation:

The given data are

Misty: 11, 13, 12, 14, 10, 16, 14

Brock: 8, 15, 10, 11, 16, 10, 9

The mean of Misty's successfully answered questions = ∑x/n = 90/7 = 12.86

Misty's data standard deviation = √(∑(x - μ)²/n) = 1.884

The mean of Brock's successfully answered questions = ∑x/n = 79/7 = 11.29

Brock's data  standard deviation = √(∑(x - μ)²/n) = 2.81

Therefore, based on the value of the standard deviation which is a measure of variability, whereby the standard deviation of Brock's number of successfully answered questions is larger than the standard deviation of Misty's number of tech supported successfully answered questions, Misty is the more consistent employee.

Answer:

[tex]2\sqrt{2} +2\sqrt{5}[/tex]

Step-by-step explanation:

i just got this one right

the kite has two pairs of congruent sides. using the distance formula, the two shorter sides=[tex]\sqrt{2}[/tex] (since there are two of those length sides, you multiply it by two). Again with the distance formula, the two longer sides=[tex]\sqrt{5}[/tex] (also multiply this by two).this gives the answer c or [tex]2\sqrt{2}+2\sqrt{5}[/tex]

Answer:

The answer is c [tex]\sqrt[2]{2}[/tex] + [tex]\sqrt[2]{5}[/tex] units. just took the test

Step-by-step explanation:

Answer:

158.73 yd

Step-by-step explanation:

A picture of the situation is needed, investigating I could find a related one, in the same way the important thing is the solution, the data can be exchanged. I attach the drawing.

Let use the formula of the law of cosine:

c ^ 2 = a ^ 2 + b ^ 2 - 2 * a * b * cos C, to solve the problem

Let the third side be c, we replace:

c ^ 2 = 375 ^ 2 + 240 ^ 2 - 2 * 375 * 240 * cos 16 °

c ^ 2 = 198225 - 173027.10

c ^ 2 = 25197.9

c = 158.73

So the distance is 158.73 yd

Answer: the right answer is 195.4

Step-by-step explanation: this guy does not what's happening

Answer:

B) 5 + 17i is your answer.

Step-by-step explanation:

In order to write this equation as a complex number in standard form, you must first simplify each term.

Apple the distributive property.

21 - 4i - 1 * 16 - (7i) + 28i

Multiply -1 by 16.

21 - 4i -16 - (7i) + 28i

Multiply 7 by -1.

21 - 4i - 16 - 7i + 28i

Now simplify by adding terms :)

Subtract 16 from 21.

5 - 4i - 7i + 28i

Subtract 7i from -4i.

5 - 11i + 28i

Add -11i and 28i.

= 5 + 17i

Answer: Intercept (b) = - 2.2567

Step-by-step explanation:

(−17,8), (−14,7), (−11,6), (−12,4), (−10,1), (−7,3), (−3,2), (−3,0), (−2,−4), (0,−2), (2,−3), (6,−5), (4,−6)

Using the online regression calculator :

ŷ = -0.60205X - 2.2567

y is the predictor variable

X - the independent variable

0.60205 = slope or gradient

- 2.2567 = intercept (b) where the line best fit cross the y-axis.

The linear regression line is made using the least-squares method. The value of b is -2.2567.

Firstly, there is a data set. Then, we try to fit a line which will tell about the linear trend. This line is made using the least-squares method.

Given the points of the data(−17,8), (−14,7), (−11,6), (−12,4), (−10,1), (−7,3), (−3,2), (−3,0), (−2,−4), (0,−2), (2,−3), (6,−5), (4,−6).

Now, Since the question states about using the technology, therefore, if we use the online regression calculator:

ŷ = -0.60205X - 2.2567

y is the predictor variable

X - the independent variable

-0.60205 is the value of m which is the slope or gradient of the regression line, while -2.2567 is the value of the intercept of the regression line.

Hence, the value of b is -2.2567.

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Answer:

Average consumption ( mean )  =  9

MOE = 4

Step-by-step explanation:

We know that

CI   ( 5  ;  13 )

and   CI [ μ - MOE  ;  μ + MOE ]

From the above relations we get

μ - MOE = 5

μ + MOE = 13

Adding member to member these two equations we get

2*μ  =  18

μ = 9    and MOE = 13 - 9

MOE = 4

Answer:

Step-by-step explanation:

To find x we use cosine

cos ∅ = adjacent / hypotenuse

From the question

The hypotenuse is x

The adjacent is 18

So we have

cos 69 = 18/x

x cos 69 = 18

Divide both sides by cos 69

x = 18/cos 69

x = 50.2

x = 50° to the nearest tenth

Hope this helps you

Answer:

f(x) = 4x² + 48x + 149

Step-by-step explanation:

Given

f(x) = 4(x + 6)² + 5 ← expand (x + 6)² using FOIL

     = 4(x² + 12x + 36) + 5 ← distribute parenthesis by 4

     = 4x² + 48x + 144 + 5 ← collect like terms

     = 4x² + 48x + 149 ← in standard form

Answer:

[tex]f(x)=4x^{2} +149[/tex]

Step-by-step explanation:

Start off by writing the equation out as it is given:

[tex]f(x)=4(x+6)^{2} +5[/tex]

Then, get handle to exponent and distribution of the 4 outside the parenthesis:

[tex]f(x)=4(x^{2} +36)+5\\f(x)=4x^{2} +144+5[/tex]

Finally, combine any like terms:

[tex]f(x)=4x^{2} +149[/tex]

Answer:

1992.50 mL; 825 mL

Step-by-step explanation:

Given that :

Capacity of bottles in the attachment = 2L

Amount of soft drink in bottle 1 = 7.50mL

Amount of soft drink in bottle 2 = 1175mL

Converting liter milliliter

1Litre = 1000 milliliters

Therefore 2Litres = 2000 milliliters

Capacity each of bottle = 2000 milliliters

Volume of drink required to completely fill bottle 1:

2000mL - 7.50mL = 1992.50 mL

Volume of drink required to completely fill bottle 2:

2000mL - 1175mL = 825 mL

a+b+c=68

b-3=a

c-5=b

now just solve the system of equations, substitue so that there are only b's in the equation:

a+b+c=68

(b-3) + b + (b+5) = 68

3b=66

b=22

Therefore Barbara is 22

The required age of barbar is 22 years.

Alice, Barbara, and Carol are sisters. Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the sisters are 68 years old.  How old is Barbara to be determined.

In mathematics, it deals with numbers of operations according to the statements.

Let the age of Alice, Barbara and Carol are a, b and c.

Age Alice is 3 years younger than Barbara,

a = b - 3     - - - -(1)

Age Barbara is 5 years younger than Carol

b = c - 5

c = b + 5     - - - -(2)

Together the sisters are 68 years old i.e.

a + b +c =68

From equation 1 and 2

b - 3 + b + b +5 = 68

3b + 2 = 68

3b = 66

b  = 33

Thus, the required age of barbar is 22 years.

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Answer:

first option

Step-by-step explanation:

Given

[tex]\frac{15}{x}[/tex] + 6 = [tex]\frac{9}{x^2}[/tex]

Multiply through by x² to clear the fractions

15x + 6x² = 9 ( subtract 9 from both sides )

6x² + 15x - 9 = 0 ( divide through by 3 )

2x² + 5x - 3 = 0 ← in standard form

Consider the factors of the product of the coefficient of x² and the constant term which sum to give the coefficient of the x- term.

product = 2 × - 3 = - 6 and sum = + 5

The factors are + 6 and - 1

Use these factors to slit the x- term

2x² + 6x - x - 3 = 0 ( factor the first/second and third/fourth terms )

2x(x + 3) - 1(x + 3) = 0 ← factor out (x + 3) from each term

(x + 3)(2x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = 0.5

Solution set is { - 3, 0.5 }

Answer: The lines are parallel.

The slopes are equal.

The y-intercepts are different.

The system has no solution.

Step-by-step explanation:

For  a pair of equations: [tex]a_1x+b_1y=c_1\\\\a_2x+b_2y=c_2[/tex]

They coincide if [tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}[/tex]

They are parallel if [tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}[/tex]

They intersect if [tex]\dfrac{a_1}{a_2}\neq\dfrac{b_1}{b_2}[/tex]

Given equations: [tex]8 x + 10 y = 30\\ 12 x + 15 y = 60[/tex]

Here,

[tex]\dfrac{a_1}{a_2}=\dfrac{8}{12}=\dfrac{2}{3}\\\\ \dfrac{b_1}{b_2}=\dfrac{10}{15}=\dfrac{2}{3}\\\\ \dfrac{c_1}{c_2}=\dfrac{30}{60}=\dfrac{1}{2}[/tex]

⇒[tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}[/tex]  

Hence, The lines are parallel.

It has no solution. [parallel lines have no solution]

Write 8 x + 10 y = 30 in the form of y= mx+c, where m is slope and c is the y-intercept.

[tex]y=-\dfrac{8}{10}x+\dfrac{30}{10}\Rightarrow\ y=-0.8x+3[/tex]

i.e. slope of 8 x + 10 y = 30 is -0.8 and y-intercept =3

Write  12 x + 15 y = 60 in the form of y= mx+c, where m is slope

[tex]y=-\dfrac{12}{15}x+\dfrac{60}{15}\Rightarrow\ y=-0.8x+4[/tex]

i.e. slope of  12 x + 15 y = 60 is -0.8 and y-intercept =4

i.e. The slopes are equal but y-intercepts are different.

Answer: The lines are parallel.

The slopes are equal.

The y-intercepts are different.

The system has no solution.

Step-by-step explanation:

For  a pair of equations:  

They coincide if  

They are parallel if  

They intersect if  

Given equations:  

Here,

⇒  

Hence, The lines are parallel.

It has no solution. [parallel lines have no solution]

Write 8 x + 10 y = 30 in the form of y= mx+c, where m is slope and c is the y-intercept.

i.e. slope of 8 x + 10 y = 30 is -0.8 and y-intercept =3

Write  12 x + 15 y = 60 in the form of y= mx+c, where m is slope

i.e. slope of  12 x + 15 y = 60 is -0.8 and y-intercept =4

i.e. The slopes are equal but y-intercepts are different.

Answer:

D. Stretch

Step-by-step explanation:

All the others keep the same dimensions

The one which is not a rigid motion transformation is D. Stretch.

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

Rigid motion transformation is the transformation which is formed when a point or a shape is transformed such that the size or the shape of the original object does not change.

In rotation, translation and reflection, there is no change in the size or the shape.

But in dilation, the size becomes smaller or larger based on it is enlargement or stretch.

So stretch is not a rigid motion transformation.

Hence option D is the correct answer.

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Answer:

A

Step-by-step explanation:

Answer:

a)2/5

Step-by-step explanation:

5:2 is correct

5/2 is nothing but 5:2

10:4 is also correct because when we simplify it we get5:2

Answer:

[tex]\displaystyle \sin \theta = \frac{4}{5}[/tex] if [tex]\displaystyle \cos\theta = -\frac{3}{5}[/tex] and [tex]\theta[/tex] is in the second quadrant.

Step-by-step explanation:

By the Pythagorean Trigonometric Identity:

[tex]\left(\sin \theta\right)^2 + \left(\cos\theta)^2 = 1[/tex] for all real [tex]\theta[/tex] values.

In this question:

[tex]\displaystyle \left(\cos\theta\right)^2 = \left(-\frac{3}{5}\right)^2 = \frac{9}{25}[/tex].

Therefore:

[tex]\begin{aligned} \left(\sin\theta\right)^2 &= 1 -\left(\cos\theta\right)^2 \\ &= 1 - \left(\frac{3}{5}\right)^2 = \frac{16}{25}\end{aligned}[/tex].

Note, that depending on [tex]\theta[/tex], the sign [tex]\sin \theta[/tex] can either be positive or negative. The sine of any angles above the [tex]x[/tex] axis should be positive. That region includes the first quadrant, the positive [tex]y[/tex]-axis, and the second quadrant.

According to this question, the [tex]\theta[/tex] here is in the second quadrant of the cartesian plane, which is indeed above the [tex]x[/tex]-axis. As a result, the sine of this

It was already found (using the Pythagorean Trigonometric Identity) that:

[tex]\displaystyle \left(\sin\theta\right)^2 = \frac{16}{25}[/tex].

Take the positive square root of both sides to find the value of [tex]\sin \theta[/tex]:

[tex]\displaystyle \sin\theta =\sqrt{\frac{16}{25}} = \frac{4}{5}[/tex].

Answer:

B. The given value is a for the because the data collected represent a . statistic year sample

Step-by-step explanation:

A population is the total of similar items that are of interest to the researcher.

Since the researcher cannot measure each of these items he chooses a part of it to measure. This part of the population is called a sample.

A good sample is representative of the larger population. Deduction made from the sample is used to represent the whole population.

In this scenario the population is the whole year, and the sample is 41 days.

So the mean derived from the sample is statistic of sample from the year.

This can be used to make deductions about the whole year.

Answer:

Hey there!

Triangle PQT and RQT are congruent by AAS. AAS means that one side is congruent, and two angles are congruent.

Since these triangles share one side, then the side is congruent.

PR is a straight line, so if angle Q is 90 degrees, then the supplementary angle is also 90 degrees.

Finally, the diagram shows that angles R and P are congruent to each other.

Hope this helps :)

Answer:

Step-by-step explanation:

x² + 2x + 1 = 0

Using the quadratic formula

[tex]x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

a = 1 , b = 2 , c = 1

We have

[tex]x = \frac{ - 2± \sqrt{ {2}^{2} - 4(1)(1)} }{2(1)} \\ \\ x = \frac{ - 2 ± \sqrt{4 - 4} }{2} \\ \\ x = \frac{ - 2 ± \sqrt{0} }{2} \\ \\ x = - \frac{2}{2} \\ \\ x = - 1[/tex]

Hope this helps you

Answer: x=35

Step-by-step explanation:

There are 720 degrees total in a hexagon. So, all of the angles should add up to that. Write out the equation

720= (4x-5)+(117)+(3x-3)+(3x+6)+(118)+(4x-3)

720=14x+230

490=14x

x=35

hope this helped you:)

Answer:

Inclusive means that we'll use the signs ≤ and ≥. Let's call the variable in our inequality as x. Therefore, the answer is -5 ≤ x ≤ -1.

Answer:

83

Step-by-step explanation:

You're given two vertical angles, and vertical angles are congruent. This means that (6x - 7) = (4x + 23); x = 15. Plug it into ABC (which is (6x - 7)) to get 6(15) - 7 = 90 - 7 = 83

Answer:

Probability of selecting none of the correct six integers:

a) 0.350

b) 0.427

c) 0.489

d) 0.540

Step-by-step explanation:

a) 40

Given:

Number of integers in a lottery  6

Order in which these integers are selected does not matter

To find:

Probability of selecting none of the correct six integers

Solution:

When the order of selection does not matter then we use Combinations.

Given integers = 40

Number of ways to choose 6 from 40.

Let A be the sample space of choosing digits 6 from 40.

Then using Combinations:

(n,k) = n! / r! (n-r)!

n = 40

r = 6

40C6

=(40,6) = 40! / 6! ( 40 - 6)!

           = 40! / 6!34!

           = 40*39*38*37*36*35*34! / 6!34!

           = 2763633600 / 720

          = 3838380

Let E be the event of selecting none of the correct six integers.

So using combinations we can find the total number of ways of selecting none of 6 integers from 40

n = 40 - 6 = 34

r = 6

34C6

=(34,6) = 34! / 6! ( 34 - 6)!

           = 34! / 6! 28!

           = 34 * 33 * 32 * 31 * 30 * 29 * 28! / 6! 28!

           =968330880 / 720

           = 1344904

Probability of selecting none of the correct six integers:

P(E) = E / A

       = 1344904 / 3838380

        = 0.350

Probability of selecting none of the correct six integers is 0.350

b) 48

Following the method used in part a)

(n,k) = n! / r! (n-r)!

n = 48

r = 6

48C6

=(48,6) = 48! / 6! ( 48 - 6)!

            = 48! / 6! ( 42 )!

            = 48*47*46*45*44*43*42! / 6!42!

            = 8835488640 / 720

            = 12271512

Let E be the event of selecting none of the correct six integers.

So using combinations we can find the total number of ways of selecting none of 6 integers from 48

n = 48 - 6 = 42

r = 6

42C6

= (42,6) = 42! / 6! ( 42 - 6)!

              = 42! / 6! 36!

              = 3776965920

              = 5245786

P(E) = E / A

       = 5245786/12271512

       = 0.427

c) 56

(n,k) = n! / r! (n-r)!

n = 56

r = 6

56C6

=(56,6) = 56! / 6! ( 56- 6)!

            = 56! / 6! ( 50 )!

            = 56*55*54*53*52*51*50! / 6! 50!

            = 23377273920/6

            = 32468436

Let E be the event of selecting none of the correct six integers.

So using combinations we can find the total number of ways of selecting none of 6 integers from 56

n = 56 - 6 = 50

(50,6) = 50! / 6! ( 50- 6)!

           = 50*49*48*47*46*45*44! / 44! 6!

           = 11441304000 / 6

           = 15890700

P(E) = E / A

       = 15890700 / 32468436

      = 0.489

d) 64

(n,k) = n! / r! (n-r)!

n = 64

r = 6

64C6

=(64,6) = 64! / 6! ( 64 - 6)!

            = 64! / 6! ( 58 )!

            = 64*63*62*61*60*59*58! / 6! 58!

            = 53981544960 / 720

            = 74974368

Let E be the event of selecting none of the correct six integers.

So using combinations we can find the total number of ways of selecting none of 6 integers from 64

n = 64 - 6 = 58

(58,6) = 58! / 6! ( 58- 6)!

           = 58*57*56*55*54*53*52! / 52! 6!

           = 29142257760/ 6

           = 40475358

P(E) = E / A

       = 40475358/ 74974368

      = 0.540

The probability of selecting none of the correct six integers in a lottery is, 0.350.

Number of integers given = 40

So, Total outcomes for choosing 6 from 40 integers.

         Number of arrangements [tex]=_{6}^{40}\textrm{C}[/tex]

                                                    [tex]=\frac{40!}{6!*34!} =3838380[/tex]

Since, we have to find probability of selecting none of the correct six integers in a lottery.

Remaining integer = 40 - 6 =34

Let favourable outcomes is selecting none of the correct six integers.

So, number of arrangements, = [tex]=_{6}^{34}\textrm{C}[/tex]

                                                 = [tex]\frac{34!}{6!*28!}=1344904[/tex]

Probability is defined as, divide favourable outcomes by total outcomes.

So, The probability of selecting none of the correct six integers in a lottery,

                            [tex]P=\frac{1344904}{3838380}=0.35[/tex]

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Answer: 85 = 3.75x + 12.25

The restaurant can have 19 loads

Step-by-step explanation:

The 85 accounts for the restaurant's budget.  The 3.75x accounts for the cost of each load.  The 12.25 accounts for the delivery fee.

85 = 3.75x + 12.25

Subtract 12.25

72.75=3.75x

Divide by 3.75

19.4=x

Round down

x = 19

Hope it helps <3

Answer:

19.4

Step-by-step explanation:

3.75x+12.25=85

subtract 12 from both sides, and divide to put the variable alone.

Then you have to get 19.53333333

Round up and its 19.4

Check if it is true

3.75×19.4+12.25=85

Answer:

The second answer

Step-by-step explanation:

Remember rise over run since this is a negative line go down 4 and over to the right 3. Now you found your slope which is -4/3. To find the y intercept simply look at the y axis and look at where the line passes through it