The sum of the first 5 terms of an AP is 30 and the sum of the four term from T6 to T9 (inclusive) is 69. Find the AP​

Answer:

C = 4

Step-by-step explanation:

solution:

f(x) can be differentiated on (0,16)

By mean value theorem

= f(16) = 4

= f(0) = 0

= f(b) - f(a)/b - a

= f(4) - f(0)/ f(16) - f(0)

= f'(c) = 1/2√C

= 1/2√C = 4/16

= 1/2√C = 1/4

= 4 = 2√C

= √C = 4/2

we make c the subject of the formula and also eliminate the square root

= √C = 2

= C = 2²

= C = 4

Answer:

ΔP = 567

Step-by-step explanation:

The increasing rate of the population is  13,51*t.

That rate by definition is:

dP/dt   where P is the population therefore

dP/dt = 13,51*t

dt  =  13,51*t*dt

Integrating on both sides of the equation  we get:

∫dp = ∫ 13,51*t*dt

P =  13,51*t²/2 + K         ( K is population for t = 0 )

Now the population in 10 years    P(₁₀)

P(₁₀) =  13,51* (10)² /2  + K

P(₁₀) =  675,5  + K      (1)

And   P(₄)     is    

P(₄)  = 13,51*(4)²/2  * K

P(₄)  = 108,08 + K        (2)

Then substracting

P(₁₀) - P(₄)  =  ( 675,5  + K ) -  ( 108,08 + K )

ΔP =  567,42

But we don´t have fraction of animal, then

ΔP = 567

Answer:

(9). Range; {8, 5, 2, -1, -4}

(10). Range; {-15, -7, 1, 9, 17}

Step-by-step explanation:

Domain of a function is (x-values) determined by the input values and Range of a function is determined by the (y-values) output values of the function.

(9). For the given function,

    f(x) = -3x + 2

    If the Domain of this function is a set of values,

    {-2, -1, 0, 1, 2}

    For Range,

    x       -2        -1         0        1       2

    f(x)     8         5        2       -1      -4

   Therefore, Range of the function 'f' will be; {8, 5, 2, -1, -4}

(11). f(x) = 4x + 1

    Domain is {-4, -2, 0, 2, 4}

    Table for input-output values will be,

    x      -4        -2         0        2        4

    f(x)  -15        -7          1        9        17

    Therefore, Range of the function will be {-15, -7, 1, 9, 17}

Answer:

B

Step-by-step explanation:

"A" is not a reflection, it looks like a translation.

"C" is not a reflection, it is a rotation.

So, B is a reflection.

Answer:

[tex]\large \boxed{\mathrm{Graph \ C}}[/tex]

Step-by-step explanation:

The reflection is across the line y = x.

All options show reflection. Option C shows reflection across the line y = x.

In the reflection, the points on the triangle will also be reflected.

Point S is reflected across the line y=x, the reflected point is S’.

Point R is reflected across the line y=x, the reflected point is R’.

Point Q is reflected across the line y=x, the reflected point is Q’.

Answer:

d. The graph of g(x) is the graph of f(x) reflected over the x-axis.

Step-by-step explanation:

The standard transformation

g(x) = - f(x)

is a simple reflection about the x-axis.

So the answer is the last option.

Answer:

Last one

Step-by-step explanation:

The function we are interested in are g(x) and f(x).

● g(x)= (-1/x)

● f(x)= 1/x

Notice what happens when we input the same values in both functions.

● g(1) = -1/1 = -1

● f(x) = 1/1 = 1

●g(2) = -1/2 = -0.5

● f(2) = 1/2 = 0.5

Notice that we get opposite values by imputing the same number.

Wich means:

●f(x) = -g(x)

So the graph of g(x) is the graph of f(x) reflected over the x axis.

Answer:

  2.5

Step-by-step explanation:

Put the values in place of the corresponding variables and do the arithmetic:

  ab - 0.5b = (1)(5) -0.5(5) = 5 - 2.5 = 2.5

Answer:

[tex]IQR=Q_{3}-Q_{1}[/tex]

Step-by-step explanation:

The inter-quartile range is a measure of dispersion of a data set.

It is the difference between the third and the first quartile.

[tex]IQR=Q_{3}-Q_{1}[/tex]

The 1st quartile (Q₁) is well defined as the mid-value amid the minimum figure and the median of the data set. The 2nd quartile (Q₂) is the median of the data. The 3rd quartile (Q₃) is the mid-value amid the median and the maximum figure of the data set.

Answer:

Yes,

Step-by-step explananation

The quotient of two rational numbers is always rational, and the reason for this lies in the fact that the product of two integers is always an rational number.

The Quotient of two Rational Numbers is a Rational Number if and only if Numerator and Denominator are Multiples.

From Algebra, we know that a Rational Number is a Real Number of the form:

[tex]x = \frac{a}{b}[/tex], [tex]a, b\in \mathbb{N}[/tex], [tex]x \in \mathbb{R}[/tex] (1)

Where:

The Quotient can be an Integer or not. In the first case, all Quotients have their equivalent Rational Numbers.

Now, if we divide a Rational Number by another Rational Number, then we have the following expression:

[tex]x' = \frac{x_{1}}{x_{2}}[/tex]

If [tex]x'[/tex] is a Rational Number, then it must also an Integer and if [tex]x'[/tex] is an Integer, then [tex]x_{1}[/tex] and [tex]x_{2}[/tex] must be Multiples of each other.

The Quotient of two Rational Numbers is a Rational Number if and only if Numerator and Denominator are Multiples.

Please see this question related to Rational Numbers: https://brainly.com/question/24398433

Answer:

c

Step-by-step explanation

Answer:

a

   [tex]P(X < 2500) = 0.02668[/tex]

b

   [tex]P(X < 1500) = 0.00001[/tex]

Step-by-step explanation:

From the question we are told that

     The  population mean  is  [tex]\mu = 3350[/tex]

      The standard deviation is  [tex]\sigma = 440[/tex]

We also told in the question that the birth weight is  approximately Normally distributed

    i.e      [tex]X \ \~ \ N(\mu , \sigma )[/tex]

Given that Low-birth-weight babies weighing less than 2500 grams,then the proportion of babies born full term are low-birth-weight babies is mathematically represented as

       [tex]P(X < 2500) = P(\frac{ X - \mu }{\sigma } < \frac{2500 - \mu}{\sigma } )[/tex]

Generally  

         [tex]\frac{X - \mu}{ \sigma } = Z (The \ standardized \ value \ of \ X )[/tex]

So

      [tex]P(X < 2500) = P(Z < \frac{2500 - \mu}{\sigma } )[/tex]

substituting values

      [tex]P(X < 2500) = P(Z < \frac{2500 - 3350}{440 } )[/tex]

       [tex]P(X < 2500) = P(Z <-1.932 )[/tex]

Now from the standardized normal distribution table(These value can also be obtained from Calculator dot com) the value of

     [tex]P(Z <-1.932 ) = 0.02668[/tex]

=>    [tex]P(X < 2500) = 0.02668[/tex]

Given that  very-low-birth-weight babies (weighing less than 1500 grams,then the  proportion of babies born full term are very-low-birth-weight babies is mathematically represented as

    [tex]P(X < 1500) = P(\frac{ X - \mu }{\sigma } < \frac{1500 - \mu}{\sigma } )[/tex]

    [tex]P(X < 1500) = P(Z < \frac{1500 - \mu}{\sigma } )[/tex]

substituting values

           [tex]P(X < 1500) = P(Z < \frac{1500 - 3350}{440 } )[/tex]

       [tex]P(X < 1500) = P(Z <-4.205 )[/tex]

Now from the standardized normal distribution table(These value can also be obtained from calculator dot com) the value of

     [tex]P(Z <-1.932 ) = 0.00001[/tex]

    [tex]P(X < 1500) = 0.00001[/tex]

Answer: At-least 89% of employees with commuting times between 54 minutes and 72 minutes .

Step-by-step explanation:

Given: Commuting times for employees of a local company have a mean of 63 minutes and a standard deviation of 3 minutes.

Now, 54 minutes = (63 - 9) minutes

= (63 -3(3)) minutes

= Mean - 3 standard deviation

72 minutes =  (63 + 9) minutes

=63 +3(3) minutes

= Mean + 3 standard deviation

According to Chebyshev's theorem, at least [tex]\dfrac{8}{9}[/tex] of the data lie within 3 standard deviations of the mean.

i.e. The percentage of employees with commuting times between 54 minutes and 72 minutes = [tex]\dfrac{8}{9}\times100\approx89\%[/tex]

Hence, at-least 89% of employees with commuting times between 54 minutes and 72 minutes .

Answer:

[tex]\large \boxed{\mathrm{B. \ \ \{-10, -6, 10\} }}[/tex]

Step-by-step explanation:

The domain is the x values.

D = {-1, 0, 4}

y = 4(-1) - 6 = -4 - 6 = -10

y = 4(0) - 6 = 0 - 6 = -6

y = 4(4) - 6 = 16 - 6 = 10

The range is the y values.

R = {-10, -6, 10}

Answer:

[tex]\large \boxed{\mathrm{4/5 \ cups}}[/tex]

Step-by-step explanation:

Subtract 1/10 from 9/10 to find out how much is left.

9/10 - 1/10

8/10 = 4/5

Answer:

Step-by-step explanation:

[tex]Volume\:of \: syrup \:in \:cup\:from\:jug = \frac{9}{10}\\\\ She \:took\: \frac{1}{10} from \:the\:cup\:into\:the \:jug \\\\Volume \:of syrup\:in\:cup=?\\\\\frac{9}{10} -\frac{1}{10} \\\\= \frac{4}{5} cups[/tex]

Answer:

The test statistic for testing if the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard is 3.234.

Step-by-step explanation:

We are given that in a random sample of 380 cars driven at low altitudes, 42 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed.

In an independent random sample of 90 cars driven at high altitudes, 24 of them exceeded the standard.

Let [tex]p_1[/tex] = population proportion of cars driven at high altitudes who exceeded a standard of 10 grams.

[tex]p_2[/tex] = population proportion of cars driven at low altitudes who exceeded a standard of 10 grams.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1\leq p_2[/tex]      {means that the proportion of high-altitude vehicles exceeding the standard is smaller than or equal to the proportion of low-altitude vehicles exceeding the standard}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1>p_2[/tex]      {means that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard}

The test statistics that will be used here is Two-sample z-test statistics for proportions;

                             T.S.  =  [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex]  ~  N(0,1)

where, [tex]\hat p_1[/tex] = sample proportion of cars driven at high altitudes who exceeded a standard of 10 grams = [tex]\frac{24}{90}[/tex] = 0.27

[tex]\hat p_2[/tex] = sample proportion of cars driven at low altitudes who exceeded a standard of 10 grams = [tex]\frac{42}{380}[/tex] = 0.11

[tex]n_1[/tex] = sample of cars driven at high altitudes = 90

[tex]n_2[/tex] = sample of cars driven at low altitudes = 380

So, the test statistics =  [tex]\frac{(0.27-0.11)-(0)}{\sqrt{\frac{0.27(1-0.27)}{90}+\frac{0.11(1-0.11)}{380} } }[/tex]      

                                   =  3.234

The value of z-test statistics is 3.234.

Step-by-step explanation:

(f+g)(x) = f(x) + g(x)

= x/2-3 + 4x²+x+4

= ..........

Answer:

1.)  [tex]\frac{1}{9^4}*9^3[/tex]

2.) [tex]\frac{1}{w^7}[/tex]

3.)

Step-by-step explanation:

When you have a negative exponent, rewrite:

[tex]x^{-a}=\frac{1}{x^a}[/tex]

Rewrite using this to change all negative exponents.

Answer:

Multiple Answers

Step-by-step explanation:

Note: When multiplying numbers with exponents, you add the exponents. When dividing numbers with exponents, you subtract exponents.When you have a negative exponent, flip the fraction and write it as a positive exponent.

1) -4 + 3= -1  

So we have  (9^-4) + (9^3)= (1/(9^1)

2) (1/w)^7

3) cannot read problem, but just apply the rules I wrote under "Note"

4) 14/y

5) cannot read problem,but just apply the rules I wrote under "Note"

6) 20d^4 n^? --Cannot read n exponents--.

7) cannot read problem

8) Cannot read problem

9) 90/z^4---only if exponents are 5,-3,and-6

10) 1/(9^5)

11) 54b^4

12) Cannot read problem

13) 16d^8c^8 ---if exponents are 5,3,6,2--

14) s^8

Hope this helps! Plz give brainly, I kinda need it.

Answer:

D. Factoring trinomials

Step-by-step explanation:

The factoring trinomials method is the best way to factor the expression, since it is in the standard trinomial form ax² + bx + c

In this method, you can factor the expression by finding 2 factors of c that add up to b.

The expression is not in the simplest form, and difference of squares cannot be used because there are no perfect squares. Prime factorization is also not used for factoring expressions with variables.

So, D is the right answer.

Answer:

1. It would take the car to get from Tucson to Phoenix 12 hours.

2. for the car to go around the equator it would take 637 hours if it is still travelling at 10km/hr.

hope this helps

Step-by-step explanation:

1. 120 km divided by 10 = 12 hours

Answer:

see below

Step-by-step explanation:

For the first question, you should multiply the scale dimension by 30 to get the actual dimension. This is because the scale is 1:30 where the scale dimension is the 1 and the actual dimension is 30, so therefore, the scale dimension is 1/30th of the actual dimension, so to get the actual dimension, we can multiply the scale dimension by 30. I'm not totally sure how to attach pictures from my phone on my computer (sorry) but an example of a drawing could be two rectangles, the first (this is the scale drawing) having dimensions of 1 by 2 units and the second (this is the actual drawing) having dimensions of 30 by 60 units. I hope this helps!

Answer:

Option (2)

Step-by-step explanation:

In an arithmetic progression,

[tex]a_1,a_2,a_3.........a_{n-1},a_n[/tex]

First term of the progression,

a = [tex]a_1[/tex]

Common difference 'd' = [tex](a_2-a_1)[/tex]

Recursive formula for the sequence,

a = [tex]a_1[/tex]

[tex]a_n=a_{n-1}+d[/tex]

By applying these rules in the recursive formula,

[tex]a_1=\frac{4}{5}[/tex]

[tex]a_n=a_{n-1}+\frac{3}{2}[/tex]

Common difference 'd' = [tex]\frac{3}{2}[/tex]

Therefore, Option (2) will be the answer.

Answer:

There is a positive correlation between X and Y.

Step-by-step explanation:

The estimated regression equation is:

[tex]\hat Y=20X+200[/tex]

The general form of a regression equation is:

[tex]\hat Y=b_{yx}X+a[/tex]

Here, [tex]b_{yx}[/tex] is the slope of a line of Y on X.

The formula of slope is:

[tex]b_{yx}=r(X,Y)\cdot \frac{\sigma_{y}}{\sigma_{x}}[/tex]

Here r (X, Y) is the correlation coefficient between X and Y.

The correlation coefficient is directly related to the slope.

And since the standard deviations are always positive, the sign of the slope is dependent upon the sign of the correlation coefficient.

Here the slope is positive.

This implies that the correlation coefficient must have been a positive values.

Thus, it can be concluded that there is a positive correlation between X and Y.

Answer:c

Step-by-step explanation:

Answer: The answer is C.

Hope this helps you!

Answer:

[tex]\bold{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}[/tex]

Step-by-step explanation:

To find:

Simplified product of:

[tex](\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})[/tex]

Solution:

First of all, let us have a look at some of the formula:

1. [tex](a+b) (c+d) = ac+bc+ad+bd[/tex]

2. [tex]a^b\times a^c =a^{b+c }[/tex]

3. [tex]\sqrt{a^{2b}} = \sqrt{a^b.a^b}=a^b[/tex]

4. [tex]\sqrt a \times \sqrt b = \sqrt{a\times b}[/tex]

Now, let us apply the above formula to solve the given expression.

[tex](\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})\\\\\Rightarrow(\sqrt{10x^4})(2\sqrt{15x^4})+(\sqrt{10x^4})(\sqrt{3x^3})-(x\sqrt{5x^2})(2\sqrt{15x^4})-(x\sqrt{5x^2})(\sqrt{3x^3})\\\\\Rightarrow2\sqrt{150x^8}+\sqrt{30x^7}-2x\sqrt{75x^6}-x\sqrt{15x^5}\\\\\Rightarrow\bold{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}[/tex]

The answer is:

[tex]\bold{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}[/tex]

Answer:

Its D

Step-by-step explanation:

Answer:

Here's one way:

4    9    2

3    5    7

8    1     6

Step-by-step explanation:

Answer:

2 * 3 + 4 * 5 = 26

5 * 7 + 1 * 8 = 43

Step-by-step explanation:

Given

_ * _ + _ * _ = _ _

Required

Fill in the boxes with digits 0 to 9

From the question we understand that the result must be two digits i.e. _ _

To solve this, we'll make use of trial by error method:

Fill the first two boxes wit 2 and 3: _ * _ becomes 2 * 3

Fill the next two boxes with 4 and 5: _ * _ becomes 4 * 5

So,we have

2 * 3 + 4 * 5

6 + 20

26

Hence, the first combination is 2 * 3 + 4 * 5 = 26

Another possible combination is:

Fill the first two boxes wit 5 and 7: _ * _ becomes 5 * 7

Fill the next two boxes with 1 and 8: _ * _ becomes 1 * 8

So,we have

5 * 7 + 1 * 8

35 + 8

43

Hence, another combination is 5 * 7 + 1 * 8 = 43

Note that; there are more possible combinations

Answer:

Using a graphing calc.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello, "the constant term has been written on the right side", it means that we add 18 to both sides to get.

[tex]x^2+3x-18=0\\\\x^2+3x=18\\\\\text{We can see the beginning of } (x+\dfrac{3}{2})^2 \\\\x^2+3x=(x+\dfrac{3}{2})^2-\dfrac{3^3}{2^2}=18\\\\(x+\dfrac{3}{2})^2=18+\dfrac{9}{4}=\dfrac{18*4+9}{4}=\dfrac{81}{4}[/tex]

Hope this helps.

Thank you.

Answer:

2.25.

Step-by-step explanation:

x^2 + 3x - 18 = 0

First, we need to write the constant on the right of the equation. So, we add 18 to both sides.

x^2 + 3x = 18.

Now, we find the number that will complete the square. It will be [tex](\frac{b}{2} )^2[/tex].

In this case, b = 3.

[tex](\frac{3}{2} )^2[/tex]

= (1.5)^2

= 2.25.

So, the number that will complete the square to solve the equation is 2.25, or 2 and 1/4, or 9/4.

Hope this helps!

Answer:

45

Step-by-step explanation:

2 digit number starts from 10 ends at 99

between 10 and 19 there is only one number whose tens digit is more than ones digit.

that is 10

between 20 and 29 there are two numbers

20 and 21

like the same

between 30 and 39 there are 3 numbers

10–19. 1

20–29. 2

30–39. 3

40–49. 4

50–59. 5

60–69. 6

70–79. 7

80–89. 8

99–99. 9

sum of first n natural numbers is n(n+1)/2

9(9+1)/2=45

Three numbers between 10 and 99 have tens places that are precisely three times larger than their one's places.

The foundation of our whole number system is place value. In this approach, the value of a digit in a number is determined by where it appears in the number.

The tens digit must be three times larger than the units digit in order to meet the requirement. The units digit can have one of the following values: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.

Since we are seeking two-digit integers, it is not possible if the unit digit is zero for the tens digit also be zero.

In the case when the unit digit is 1, the tens digit must be 3, resulting in the number 31. Similar to the previous example, if the unit digit is 2, the tens digit must be 6, resulting in the number 62.

As we proceed, we discover the following integers meet the condition:

31, 62, 93

Therefore, there are three numbers from 10 to 99 that have a tens place exactly 3 times greater than their one's place.

Learn more about place values here:

https://brainly.com/question/27734142

#SPJ3