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Answer:

x=5

Step-by-step explanation:

x^3 = 125

Take the cubed root of each side

x^3 ^ (1/3) = 125 ^ (1/3)

x = 5

Answer:

53.06°F

Step-by-step explanation:

Given the equation of best fit :

y=-3.32x +97.05.

The average temperature for a month with 13.25 inches of Rainfall

Amount of Rainfall = x

Average temperature = y

To make our prediction ; put x = 13.25 in the equation and solve for y ;

y = -3.32x +97.05

Put x = 13.25

y = -3.32(13.25) +97.05

y = - 43.99 + 97.05

y = 53.06°F

Answer:

3 hrs

Step-by-step explanation:

5 * 24 = 120 miles

64x = 120 + 24x

40x = 120

x = 3 hrs

a hour,.....................

Step-by-step explanation:

let a=mangoes are delicious

b=mangoes are expensive

the symbolic form is a^b

Answer:

[tex]ac - bd[/tex]

Step-by-step explanation:

[tex]ac - bd [/tex]

Step-by-step explanation:

6t-12+15t | 25+15t

21t-12 | 25+15t

21t-12 < 25+15t

hence proved..

Answer:

21t - 12 < 25 + 15t

Step-by-step explanation:

6( t - 2 ) + 15t < 5 ( 5 + 3t )

6t - 12 + 15t < 25 + 15t

21t - 12 < 25 + 15t.

Hence , Proved.

Answer:

sensory measurement are lower after hypnotism

Step-by-step explanation:

Given the data :

Before 6.6 6.5 9.0 10.3 11.3 8.1 6.3 11.6

After 6.8 2.4 7.4 8.5 8.1 6.1 3.4 2.0

The difference ;

After - Before, d = 0.2, - 4.1, - 1.6, - 1.8, - 3.2, - 2, - 2.9, - 9.6

Hypothesis :

H0 : μd = 0

H0 : μ < 0

The test statistic ;

T = μd / sd/√n

Where, xd = mean of difference

sd = standard deviation of difference

n = sample size

Mean of difference, μd = Σx/n = - 3.13

Standard deviation of difference, sd = 2.91

T = - 3.13 / 2.91/√8

T = - 3.13 / 1.0288403

T = - 3.042

α = 0.01

The Pvalue using a Pvalue calculator ;

Degree of freedom, df = n - 1 ; 8-1 = 7

Pvalue(-3.042, 7) = 0.00939

Pvalue < α ; we reject the null and conclude that sensory measurement are lower after hypnotism

The equation "a - 3x = 0" is correctly written because it follows the standard format of an algebraic equation.

Given that,

All the equations are,

1. a + 0.2x

2. 5b - 5x + 2

3. a - 3x = 0

Now, from equation ''a - 3x = 0'',

In this equation, the variable "a" subtracted from 3 times the variable "x" equals zero.

The equal sign (=) indicates that the expression on both sides of the equation is equivalent.

The equation is properly balanced and expresses equality between the two sides.

It accurately represents a relationship between the variables "a" and "x" where the value of "a" is dependent on the value of "x" in order to satisfy the equation.

So, The correctly written algebraic equation is:

a - 3x = 0

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Answer:

[tex]f(h(xc)) = 2xc-4[/tex]

Step-by-step explanation:

Given

[tex]f(x) = x - 7[/tex]

[tex]h(x) = 2x + 3[/tex]

Required

[tex]f(h(xc))[/tex]

First, calculate h(xc)

If [tex]h(x) = 2x + 3[/tex]

Then

[tex]h(xc) = 2xc + 3[/tex]

Solving further:

[tex]f(x) = x - 7[/tex]

Substitute h(xc) for x

[tex]f(h(xc)) = h(xc) - 7[/tex]

Substitute [tex]h(xc) = 2xc + 3[/tex]

[tex]f(h(xc)) = 2xc + 3 - 7[/tex]

[tex]f(h(xc)) = 2xc-4[/tex]

Answer:

The probability of observing between 43 and 64 successes=0.93132

Step-by-step explanation:

We are given that

n=100

p=0.50

We have to find the probability of observing between 43 and 64 successes.

Let X be the random variable  which represent the success of population.

It follows binomial distribution .

Therefore,

Mean,[tex]\mu=np=100\times 0.50=50[/tex]

Standard deviation , [tex]\sigma=\sqrt{np(1-p)}[/tex]

[tex]\sigma=\sqrt{100\times 0.50(1-0.50)][/tex]

[tex]\sigma=5[/tex]

Now,

[tex]P(43\leq x\leq 64)=P(42.5\leq x\leq 64.5)[/tex]

[tex]P(42.5\leq x\leq 64.5)=P(\frac{42.5-50}{5}\leq Z\leq \frac{64.5-50}{5})[/tex]

[tex]=P(-1.5\leq Z\leq 2.9)[/tex]

[tex]P(42.5\leq x\leq 64.5)=P(Z\leq 2.9)-P(Z\leq- 1.5)[/tex]

[tex]P(42.5\leq x\leq 64.5)=0.99813-0.06681[/tex]

[tex]P(43\leq x\leq 64)=0.93132[/tex]

Hence, the probability of observing between 43 and 64 successes=0.93132

Answer:

1) 0.6838

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]

35.45% of small businesses experience cash flow problems in their first 5 years.

This means that [tex]p = 0.3545[/tex]

Sample of 530 businesses

This means that [tex]n = 530[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.3545[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.3545(1-0.3545)}{530}} = 0.0208[/tex]

What is the probability that between 34.2% and 39.03% of the businesses have experienced cash flow problems?

This is the p-value of Z when X = 0.3903 subtracted by the p-value of Z when X = 0.342.

X = 0.3903

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.3903 - 0.3545}{0.0208}[/tex]

[tex]Z = 1.72[/tex]

[tex]Z = 1.72[/tex] has a p-value of 0.9573

X = 0.342

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

[tex]Z = \frac{0.342 - 0.3545}{0.0208}[/tex]

[tex]Z = -0.6[/tex]

[tex]Z = -0.6[/tex] has a p-value of 0.27425

0.9573 - 0.2743 = 0.683

With a little bit of rounding, 0.6838, so option 1) is the answer.

Step-by-step explanation:

x intercept=(-1,0) because the graph is passing this point on the x axis

y intercept=(0,-3)

Answer:

4th option

Step-by-step explanation:

The x- intercept is where the graph crosses the x- axis.

This is at (- 1, 0 )

The y- intercept is where the graph crosses the y- axis.

This is at (0, - 3 )

Answer:

925



Step-by-step explanation:

Formula =592 x 100/64 = 925

Answer:

absolute value of the determinant, adjacent to, equal to

Step-by-step explanation:

The absolute value of a determinant  of the [tex]\text{matrix whose}[/tex] columns are the vectors and they define the [tex]\text{sides}[/tex] of a [tex]\text{parallelogram}[/tex] which is adjacent to  one another and is equal to the [tex]\text{area}[/tex] of the [tex]\text{parallelogram}[/tex].

The determinant is a real number. They are like matrices, but we use absolute value bars to show determinants whereas to represent a matric, we use square brackets.

Answer:

£2120.27

Step-by-step explanation:

A = P (1 + r100)

A = 2000 (1+ 0.03/365)^365(2)

A = 2000 ( 1.00008)^730

A = 2000 (1.060)

A = £2120.27

Answer:

first option : sqrt(26) + 6 units

Step-by-step explanation:

distance office to supermarket OS

OS² = (-7 - -2)² + (-5 - -6)² = (-7+2)² + (-5+6)² = (-5)² + 1² =

= 25 + 1 = 26

OS = sqrt(26)

distance supermarket to home SH

SH² = (-2 - 4)² + (-6 - -6)² = (-6)² + 0² = 36

SH = 6

so in total she travels sqrt(26) + 6 units

Answer:

24,48,72

Step-by-step explanation:

multiples of 6- 6,12,18,24,30,36,42,48,54,60,66,72

multiples of 8- 8,16,24,32,40,48,56,64,74,80

Answer:

2000

Step-by-step explanation:

2225 to the nearest 100 is 2300 but 3

<5 so it is 2000

Consider the below figure attached with this question.

Given:

The transformation is:

[tex]f(x,y)=(-2x,-3y+1)[/tex]

The range is (4,-2), (2, −5), (−6, 4).

To find:

The domain of the transformation.

Solution:

We have,

[tex]f(x,y)=(-2x,-3y+1)[/tex]

For the point (4,-2),

[tex](-2x,-3y+1)=(4,-2)[/tex]

On comparing both sides, we get

[tex]-2x=4[/tex]

[tex]x=\dfrac{4}{-2}[/tex]

[tex]x=-2[/tex]

And,

[tex]-3y+1=-2[/tex]

[tex]-3y=-2-1[/tex]

[tex]-3y=-3[/tex]

[tex]y=\dfrac{-3}{-3}[/tex]

[tex]y=1[/tex]

So, the domain of (4,-2) is (-2,1).

Similarly,

For the point (2,-5),

[tex](-2x,-3y+1)=(2,-5)[/tex]

On comparing both sides, we get [tex]x=-1,y=2[/tex]. So, the domain of (2,-5) is (-1,2).

For the point (-6,4),

[tex](-2x,-3y+1)=(-6,4)[/tex]

On comparing both sides, we get [tex]x=3,y=-1[/tex]. So, the domain of (-6,4) is (3,-1).

So, the domain of the given transformation is (-2, 1), (-1, 2), (3, -1).

Therefore, the correct option is A.

Answer:

|a|

Step-by-step explanation:

For any positive or negative a, when you square it, the answer is positive.

The square root symbol means the principal square root. For a positive number, the principal square root is positive. To make sure the square root is always non-negative, use absolute value.

Answer: |a|

Answer:

It's the last one

Step-by-step explanation:

(3x-1)-(x²+4)

3x-1-x²-4

-x²+3x-5

Answer:

8.35714285714

Step-by-step explanation:

Hope it help you

Answer:

Step-by-step explanation:

3(x + 1 ) =2x - 5                           This is the way the equation reads. Remove the brackets.

3x + 3 = 2x - 5                            Subtract 2x from both sides

-2x         -2x

x + 3 = - 5                                   Subtract 3 from both sides.

   -3      -3

x = - 8

Answer:

The maximum value of the objective function is 112 when x = 0 and y = 7.

Step-by-step explanation:

Given the constraints:

5x+3y≤37, 3x+5y≤35, x≥0, y≥0

Plotting the above constraints using geogebra online graphing tool, we get the solution to the constraints as:

A(0, 7), B(7.4, 0), C(5, 4) and D(0, 0)

The objective function is given as E =2x+16y, therefore:

At point A(0, 7):  E = 2(0) + 16(7) = 112

At point B(7.4, 0): E = 2(7.4) + 16(0) = 14.8

At point C(5, 4): E = 2(5) + 16(4) = 74

At point D(0, 0): E = 2(0) + 16(0) = 0

Therefore the maximum value of the objective function is at A(0, 7).

The maximum value of the objective function is 112 when x = 0 and y = 7.

Answer:

[tex]\frac{3v}{a^{2}} = h[/tex]

Step-by-step explanation:

[tex]v = \frac{1}{3} a^{2} h[/tex]

[tex]3v = a^{2} h[/tex]

[tex]\frac{3v}{a^{2}} = h[/tex]

Answer:

44

Step-by-step explanation:

Let x represent the number.

Create an equation, and solve for x:

4x = 6x - 88

-2x = -88

x = 44

So, the number is 44.

The number is 44.

To find the number.

science that deals with the addition, subtraction, multiplication, and division of numbers and properties and manipulation of numbers. Arithmetic is the basics of the abstract science of numbers and operations on them. The formula for any arithmetic sequence is this: an = a1 + d (n - 1).

Given that:

Let x represent the number.

Create an equation, and solve for x:

4x = 6x - 88

-2x = -88

x = 44

So, the number is 44.

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