Evaluate the expression when c = 3 and x= -5,
-C+5x​

Answer:

The first term is 6; the common difference in 0.8.

Step-by-step explanation:

The nth term is:

[tex] a_n = a_1 + (n - 1)d [/tex]

The sum of the first n terms is:

[tex] S_n = \dfrac{n(a_1 + a_n)}{2} [/tex]

[tex] a_{n} = a_1 + (n - 1)d [/tex]

[tex] a_{11} = a_1 + (11-1)d [/tex]

[tex] a_1 + 10d = 14 [/tex]        Equation 1

[tex] S_n = \dfrac{n(a_1 + a_n)}{2} [/tex]

[tex] S_{26} = \dfrac{26(a_1 + a_{26})}{2} [/tex]

[tex] \dfrac{26(a_1 + a_1 + 25d}{2} = 416 [/tex]

[tex] \dfrac{52a_1 + 650d)}{2} = 416 [/tex]

[tex] 26a_1 + 325d = 416 [/tex]        Equation 2

Equation 1 and Equation 2 form a system of equations in 2 unknowns.

To eliminate a_1, subtract 26 times Eq. 1 from Eq. 2.

[tex] 65d = 52 [/tex]

[tex] d = \dfrac{52}{65} [/tex]

[tex] d = \dfrac{4}{5} = 0.8 [/tex]

[tex] a_1 + 10d = 14 [/tex]

[tex] a_1 + 10 \times 0.8 = 14 [/tex]

[tex] a_1 + 8 = 14 [/tex]

[tex] a_1 = 6 [/tex]

Answer:

The first term is 6; the common difference in 0.8.

Answer:

D. None of the above

Step-by-step explanation:

Both triangles have the same shape but different size. Their area cannot be the same. Also, the ratio of their corresponding side lengths are the same.

Thus:

8/4 = 10/5 = 6/3 = 2

This implies that both triangles are similar.

Therefore, both triangles cannot have the same area, they are not of the same size and cannot be congruent to each other.

Answer:

26.32%

Step-by-step explanation:

The probability that both children are boys would be a sequence of events. Therefore, in order to calculate this we need to multiply the probability of the first baby being a boy with the probability of the second baby being a boy. Since the probability of any baby being a boy is 51.3%, we simply multiply this value in decimal form by itself.

51.3 / 100 = 0.513

0.513 * 0.513 = 0.263169 or 26.32%

Answer:

The z-score for this data is Z = -0.26.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

This is based on knowledge that in the U.S., the mean PAL is 1.65 and the standard deviation is 0.55.

This means that [tex]\mu = 1.65, \sigma = 0.55[/tex]

A study took a random sample of 51 people who lived in low income neighborhoods and found their mean PAL to be 1.63.

This means that [tex]n = 51, X = 1.63[/tex]

Using a one-sample z test, what is the z-score for this data

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{1.63 - 1.65}{\frac{0.55}{\sqrt{51}}}[/tex]

[tex]Z = -0.26[/tex]

The z-score for this data is Z = -0.26.

Answer:

1

Step-by-step explanation:

3^0

Anything raised to the zero power is 1

3^0 =1

Answer:

1

Step-by-step explanation:

Anything to the power of 0 is 1

Eg: 5⁰ = 1

a⁰= 1

(-12)⁰ = 1

Answer:

0.25

Step-by-step explanation:

Given that :

Mean score, μ = 69

Standard deviation, σ = 4

Score, x = 64

The standardized score, Zscore can be obtained using the formular :

Zscore = (x - μ) / σ

Zscore = (69 - 68) / 4

Zscore = 1 / 4

Zscore = 0.25

Answer:

Outlier therefore could only be values below  - 12.75

or could only be values above + 121.125

Step-by-step explanation:

0, 4, 6, 14, 17

inner quartile range of 0 - 17 is 1/2 of 17 subtracted from the higher number = 17 - 1/2 of 8.5 =  8.5 - 4.25 = 4.25 - 4.25 x 3

= 4.25 to 12.75 for inner quartile

inner quartile range is 12.75-4.25 = 8.5

We then 1.5 x 8.5 to show the outlier

= 12.75 meaning there is no outlier if is below.

Lower quartile fences  = 4.25 - 1.5 = 2.75

or -1.5 x 8.5 (the range) =   -12.75

Upper quartile fence = 12.75 + 1.5 = 14.25 x 8.5 =   121.125  this would be an outlier if it is 12.75 higher than 121.125 or 12.75 lower than 5.50.

Outlier therefore could only be values below  - 12.75

or could only be values above + 121.125

An observation is considered an outlier if it exceeds a distance of 1.5 times the interquartile range (IQR) below the lower quartile or above the upper quartile. The values of the lower quartile - 1.5 x IQR and upper quartile + 1.5 x IQR are known as the inner fences.

An observation is an outlier if it falls more than above the upper quartile or more than below the lower quartile. The minimum value is so there are no outliers in the low end of the distribution. The maximum value is so there are no outliers in the high end of the distribution.

Answer:

24

Step-by-step explanation:

18 times 5 is 90 so that means that the given numbers have to add up to 90 (including x)

so,

6+10+20+30=66

90-66=24

I hope this helps!

Answer:

[tex]x = 24[/tex]

Step-by-step explanation:

[tex]6 + 10 + x + 20 + 30 = 18[/tex]

There are 5 numbers that we must add to average out to get 18 so let set this equation up

[tex] \frac{6 + 10 + x + 20 + 30}{5} = 18[/tex]

[tex]6 + 10 + x + 20 + 30 = 90[/tex]

[tex]x = 24[/tex]

Answer:

x = 2.7

Step-by-step explanation:

The given equation is :

[tex](3x)^2-10=56[/tex]

We need to solve it for x.

It can be rewrite as follows:

[tex]9x^2-10=56[/tex]

Adding 10 to both sides,

[tex]9x^2-10+10=56+10\\\\9x^2=66\\\\x=\sqrt{\dfrac{66}{9}}\\\\x=2.70[/tex]

So, the value of x is equal to 2.7.

Answer:

The probability that Swallows will win the trophy is 0.8064

The probability that Rucks will win the trophy is 0.1936

Step-by-step explanation:

For each game, there are only two possible outcomes. Either the Swallows win, or they do not. The probability of them winning a game is independent of any other game, which means that the binomial probability distribution is used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Probability the Swallows wins is 0.56

This means that [tex]p = 0.56[/tex]

2 games:

This means that [tex]n = 2[/tex]

The probability that Swallows will win the trophy is

Probability they win at least one game, so:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{2,0}.(0.56)^{0}.(0.44)^{2} = 0.1936[/tex]

Then

[tex]P(X \geq 1) = 1 - 0.1936 = 0.8064[/tex]

0.8064 = 80.64% probability the Swallows win the trophy and 0.1936 probability that the Rucks win the trophy.

Answer:

b. mutually exclusive.

Step-by-step explanation:

The given description is an illustration of mutually exclusive events.

Take for instance, when you roll a die;

It is impossible to have an outcome of 2 and 6 at the same time; these means that 2 and 6 are mutually exclusive.

In a nutshell, when two or more sates of events/states of nature can not happen at the same time; such events/states of nature are mutually exclusive.

Answer:

1.92755 ,1.870320 i hope it will help you

Answer:

First bag's unit price=$1.92 per kg  Second bag's unit price=$1.87 per kg

Step-by-step explanation:

1.92 becomes 1.93

Answer:

Since you didn't mention which question.

Step-by-step explanation:

13.

[tex]1.\overline{52}\\[/tex] = 1.525252...

Let x = 1.525252...

    10x = 15.2525252....

    100x = 152.525252...

100x - x = 151.00

99x = 151

[tex]x = \frac{151}{99}\\\\or\\\\x = 1 \frac{52}{99}[/tex]

14.

4x + 10 = 8x - 26                        [ corresponding angles are congruent ]

4x - 8x = - 26 - 10

- 4x = - 36

[tex]x = \frac{-36}{-4} \\\\x = 9[/tex]

15.

Given breadth of a rectangle is ( 2/3) its length.

Let the length be x

Therefore, breadth = ( 2 /3) of x

                             [tex]= \frac{2}{3} \times x\\\\=\frac{2}{3}x[/tex]

Given perimeter = 40m

Perimeter of a rectangle = 2( length + breadth)

                                [tex]40 = 2 (x + \frac{2}{3}x )\\\\\frac{40}{2} = \frac{2}{2}(x + \frac{2}{3}x)\\\\20 = x + \frac{2}{3}x\\\\20 = \frac{3x + 2x}{3}\\\\20 \times 3 = 5x \\\\x = \frac{60}{5}\\\\x = 12\\\\Therefore, Length = x = 12 \ m \ and \ breadth = \frac{2}{3}x = \frac{2}{3} \times 12 = 8 \ m[/tex]

16.

Sum of the angles of a triangle = 180°

Given ratio = 2 : 3 : 4

Sum of the ratio = 9

Therefore,

            [tex]first \ angle = \frac{2}{9} \times 180 = 2 \times 20 = 40 ^\circ\\\\Second \ angle = \frac{3}{9} \times 180 = 3 \times 20 = 60^\circ\\\\Third angle = \frac{4}{9} \times 180 = 4 \times 20 = 80^\circ[/tex]

17.

Sum of interior angles of a polygon with n sides = ( n - 2) x 180°

Given polygon is pentagon, that is n = 5

Therefore, sum of the interior angles = ( 5 - 2) x 180 = 3 x 180 = 540°

That is ,

          x + 125 + 125 + 88 + 60 = 540°

          x + 398 = 540°

          x = 540 - 398

          x = 142°

Answer:

Please can you say which question?

Thank you

Answer:

(0, -1)

Step-by-step explanation:

It's helpful if we think of slope in the context of rise over run.

Since the point (1, 1) lies on the line, because of the slope 2, if we subtract x by 1 to get to x = 0, then we'll be subtracting y by 2.

By that logic, the answer must be (0, -1).

Answer:

sorry i cannot help you

Answer:

Distance between Amber and Claire's house = 17.63 blocks

Step-by-step explanation:

In this graph three points are showing the locations of Amber's, Betsey's and Claire's houses.

Each unit on the graph represents 1 block.

Amber walks from her house to Claire's house, then on to Betsey's house.  

We have to calculate the distance covered by Amber.

Since Distance from Claire's house to Betsey's house = 7 blocks = 7 units

and distance between Amber and Betsey's house = 8 blocks = 8 units

Now we will calculate the distance between Amber and Claire's house by Pythagoras theorem.

Distance² = 7² + 8² = 49 + 64 = 113

Distance = √113 units = 10.63 units

Therefore, total distance walked by Amber = 10.63 + 7 = 17.63 units = 17.63 blocks

Answer:

the answer might be 17. 63 because there are 7 blocks in between them so try that sorry if its wrong

Answer:

Option C

Step-by-step explanation:

Suppose that we have a given proposition p

We define the complement as:

"NOT p" or ¬p

So, if p is:

the dog is red

the complement is

the dog is NOT red.

The principal rule to work with this is:

if p is true, then ¬p is false

if p is false, then ¬p is true.

Here the proposition is:

p = "When 100 engines are shipped, all of them are free of defects."

When this is this is true, ¬p must be false.

when this is false, ¬p must be true.

Let's analyze the given options, first the incorrect ones:

A: "At most one of the engines is defective."

here if we have for example, two defective engines, then this proposition and the original proposition are false.

B: " All of the engines are defective."

Here if there is one defective engine, then this is false, and also is the original proposition.

D: "None of the engines are defective"

When the original proposition is true "When 100 engines are shipped, all of them are free of defects.", this proposition is also true (because none of the engines are defective)

Finally, the corrrect one

C "At least one of the engines is defective"

When the original proposition is true, there are no defective engines, so this is false.

While, if this is true, there is at least one defective engine, so the original proposition is false.

Then this is the correct option:

¬p = "At least one of the engines is defective"

Actual data table :

X __ y

2 15

6 13

7 9

8 8

12 5

Answer:

0.953

Step-by-step explanation:

The question isnt well formatted :

The actual data:

X __ y

2 15

6 13

7 9

8 8

12 5

Using a correlation Coefficient calculator, the correlation Coefficient obtained by fitting the data is 0.953 which depicts a strong linear correlation between the x and y variable. This shows that the value of y increases with a corresponding increase in x values and vice versa.

Answer:

Hello dude

[tex] - 1 \frac{21}{24} + 1 \frac{22}{24} = + \frac{1}{24} [/tex]

so it's positive

HAVE A NİCE DAY

Step-by-step explanation:

GREETİNGS FROM TURKEY ツ

Answer: 36in2

Step-by-step explanation:

A= base *height

=12*3

=36

The Area of the figure is 36 in².

The area of a parallelogram refers to the total number of unit squares that can fit into it and it is measured in square units (like cm2, m2, in2, etc). It is the region enclosed or encompassed by a parallelogram in two-dimensional space.

The area of a parallelogram can be calculated by multiplying its base with the altitude. The base and altitude of a parallelogram are perpendicular to each other. The formula to calculate the area of a parallelogram can thus be given as,

Area of parallelogram = b × h square units

where,

b is the length of the base

h is the height or altitude

Given:

base= 12 in

height= 3 in

Area of parallelogram,

= base * height

=12* 3

= 36 in²

Learn more about Area of parallelogram here:

https://brainly.com/question/16052466

#SPJ2

Given:

The nth term of a sequence is:

[tex]n^2+5[/tex]

To find:

The first five terms of the given sequence.

Solution:

The given sequence is:

[tex]a_n=n^2+5[/tex]

For n=1,

[tex]a_1=1^2+5[/tex]

[tex]a_1=1+5[/tex]

[tex]a_1=6[/tex]

For n=2,

[tex]a_2=2^2+5[/tex]

[tex]a_2=4+5[/tex]

[tex]a_2=9[/tex]

For n=3,

[tex]a_3=3^2+5[/tex]

[tex]a_3=9+5[/tex]

[tex]a_3=14[/tex]

For n=4,

[tex]a_4=4^2+5[/tex]

[tex]a_4=16+5[/tex]

[tex]a_4=21[/tex]

For n=5,

[tex]a_5=5^2+5[/tex]

[tex]a_5=25+5[/tex]

[tex]a_5=30[/tex]

Therefore, the first five terms of the given sequence are 6, 9, 14, 21, 30.

Answer:

It means that there are two answers, a positive one and a negative one.

Step-by-step explanation:

If you get +-5, then you have two answers: +5 and -5

Answer:

their sizes vary

Step-by-step explanation:

their sizes vary

round 5.7255 to thousands place

place after thousands place (5) rounds up the 5 before it

therefore 5.726 ur ans

MARK above ANS as branliest

Answer:

[tex]\displaystyle y - \frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{2} \bigg( x - \frac{\pi}{4} \bigg)[/tex]

General Formulas and Concepts:

Algebra I

Coordinates (x, y)

Functions

Function Notation

Point-Slope Form: y - y₁ = m(x - x₁)

Pre-Calculus

Calculus

Derivatives

Derivative Notation

Trig Derivative:                                                                                                          [tex]\displaystyle \frac{d}{dx}[sin(u)] = u'cos(u)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = sin(x)[/tex]

[tex]\displaystyle x = \frac{\pi}{4}[/tex]

Step 2: Differentiate

Step 3: Find Tangent Slope

Step 4: Find Tangent Equation

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

Answer:

not equivalent

equivalent

not equivalent

Step-by-step explanation:

25 is by itself already 5²

therefore

[tex] {25}^{m} = {5}^{2m} [/tex]

when we divide one time by 5, we simply take away 1 from the power making it

[tex] {5}^{2m - 1} [/tex]

the other options are wrong

[tex] {25}^{m - 1} [/tex]

would be right, if we have

[tex] {25}^{m} \div 25[/tex]

but we don't.

and

[tex] {25}^{2m - 1} [/tex]

would even square

[tex] {25}^{m} [/tex]

and then divide by 25. no, the original excision is nothing like that.

Answer:

270 plates

Step-by-step explanation:

First, you need to find how much one plate costs.

6x = 54

----    ----

6       6

x = 9

Now, multiply 30 plates with x, which is 9.

30(9) = 270

The answer is 270.

Answer:

270

Step-by-step explanation:

54($)÷6= 9 then 9×30=270

Answer:

Step-by-step explanation:

multiplication of two rational numbers produce a rational number.

Answer:

Range:

UCL = 4.73

LCL = 18.08

MEAN :

UCL = 27.115

LCL = 31.219

Step-by-step explanation:

Given the data:

The mean and range of each sample :

Sample __ Thread wear __ xbar __ R

1 ___31 __ 42 ___ 28 ____ 33.67 _14

2___ 26 _ 18 ____35____ 26.33 _17

3___25 __30 ___ 34____29.67 _ 9

4 __ 17 __ 25 ___ 21 _____ 21 ___ 8

5 __ 38 _ 29 ___ 35 _____ 34 __ 9

6 __ 41 __42 ___36 _____39.67_ 6

7 __ 21 __ 17 ___29 _____22.33 _12

8 __ 32 __26___28 ____ 28.67 _ 6

9 __ 41 __ 34 __ 33 ______ 36 __8

10__29___17___30 _____25.33_ 13

11 __26 __ 31 __ 40 _____32.33_ 14

12__23 __ 19 __ 45 _____12.33 __6

13 __17 __ 24 __ 32_____24.33__15

14 __43__ 35___17_____ 31.67 _ 26

15__18 ___25__ 29_____ 24 ___ 11

16__30___42___31 ____34.33__ 12

17__28___36 __ 32____ 32 ____8

18__40 __ 29 __ 31 ____33.33 __ 11

19__18 ___29__ 28____ 25 ____11

20_ 22 __ 34 __ 26 ___ 27.33 __12

Size per sample, sample size, n = 3

Number of samples, k = 20

We calculate the sample mean and range average :

Sample mean, x-- = Σxbar/n = 29.167

Range average, Rbar = ΣR/n = 11.4

The mean control limit :

x-- ± A2Rbar

From the x chart ;

A2 for n = 20 is A2 = 0.180

29.167 ± 0.180(11.40)

LCL = 29.167 - 0.180(11.40) = 27.115

UCL = 29.167 + 0.180(11.40) = 31.219

The Range control limit :

Rbar(1 ± 3(d3/d2))

From the R-chart :

d2 at n = 20 ; d2 = 3.735

d3 at n = 20 ; d3 = 0.729

LCL = 11.40(1 - 3(0.729/3.735)) = 4.725

UCL = 11.40(1 + 3(0.729/3.735)) = 18.075