What is 2 log (5x) +1/3 log (x2+6

Answer:

The distance from the boathouse to the cabin = 50 yd (nearest yard)

Step-by-step explanation:

The question is incomplete.

Question:

To find the distance from the

boathouse on shore to the cabin on the island, a surveyor measures from the boathouse to point X as shown. He then finds m∠X with an instrument called a transit. Use the surveyor’s

measurements to find the distance from the boathouse to the cabin.

Find attached the diagram of the question.

Solution:

Let the distance from the boathouse to the cabin = y

the distance from the boathouse to the point X = 30yard

Find attached the diagram for the solution.

From the diagram, the triangle is a right angled triangle

Opposite = y

Adjacent = 30yd

∠X = 59°

Using trigonometry (SohCahToa)

We would apply Toa since adjacent is given and we are looking for opposite

tan θ = opposite/adjacent

tan 59° = y/30

y = 30 tan 59

y = 30(1.6643)

y = 49.929

y = 50 yd (nearest yard)

The distance from the boathouse to the cabin = 50 yd (nearest yard)

Answer:

add x

Step-by-step explanation:

get the constants on one side, and the variables on the other for easiest solving.

Answer:

The chord is bisected

Step-by-step explanation:

The chord of a circle is a segment whose endpoints are on the circle. when a perpendicular bisector ( the radius) of any chord passes through the center of the chord at right angle to the chord, the chord is bisected into two. This is a way or could give us a good way to find the center of any circle.

     kindly find attached a diagram for your reference

Answer:

B

Step-by-step explanation:

Answer:

ooga booga ooga booga ooga booga ooga booga ooga booga

Step-by-step explanation:

Answer:

Step-by-step explanation:

1). y + 2x < 6

  (y + 2x) - 2x < 6 - 2x

   y < -2x + 6 [Slope intercept form of the inequality]

2). y + 2x < 6

  Since there is no sign of equal to (=) in the given inequality therefore, line graphed will be dashed.

Notation of less than (<) denotes the area down the line.

Option (4) will be the answer.

3). y + 2x < 6

    x ≤ 2

Please find the graph attached.

Answer:

(i) See attached image file

(ii) Option A

Step-by-step explanation:

See attached image file

Answer:

The aquarium contains [tex]\frac{x}{2}[/tex] cubic inches of water

Step-by-step explanation:

Given: A local aquarium is filled halfway with water.

To find: Volume of water in the aquarium

Solution:

Volume refers to the three-dimensional space enclosed by a boundary. S.I. unit of volume is [tex]m^3[/tex]

Let x cubic inches denotes volume of an aquarium.

As a local aquarium is filled halfway with water,

the aquarium contains [tex]\frac{x}{2}[/tex] cubic inches of water.

Answer:

Step-by-step explanation:

Showing results for The aquarium contains cubic inches of waterStep-by-step explanation:Given: A local aquarium is filled halfway with water.To find: Volume of water in the aquarium Solution:Volume refers to the three-dimensional space enclosed by a boundary. S.I. unit of volume is Let x cubic inches denotes volume of an aquarium.As a local aquarium is filled halfway with water,the aquarium contains cubic inches of water.

Answer:

52+n=m

Step-by-step explanation:

Answer:

6.5 /52 m = n

Step-by-step explanation:

The rate is 6.5 miles / 52 minutes

We are going to run m miles in n minutes

m = 6.5 / 52 * n

We want to solve for n

Multiply each side by 52/ 6.5

6.5 /52 m = 6.5 / 52 * n * 6.5 / 52

6.5 /52 m = n

Answer:

135

Step-by-step explanation:

volume = width*length*height

5*9*3=135

we need 135inches³ to paint it

Answer:

A

Step-by-step explanation:

Given Information:

Cost price = $4

Selling price = $10

Salvage value = $1.50

Average demand = μ = 250 boxes

Standard deviation = σ = 34 boxes

Required Information:

Number of lettuce boxes = ?

Answer:

The supermarket should purchase 268 boxes  of lettuce

Step-by-step explanation:

The required number of lettuce boxes that supermarket should purchase is given by

Number of lettuce boxes = μ + (z*σ)

Where μ is the average demand of lettuce boxes, σ is the standard deviation, and z is the z-score which is given by

p = C_us/(C_us + C_os)

The z-score corresponding to probability p will be obtained.

The cost of under stocking is given by

C_us = Selling price - Cost price

C_us = $10 - $4

C_us = $6

The cost of over stocking is given by

C_os = Cost price - Salvage value

C_os = $4 - $1.50

C_os = $2.50

p = C_us/(C_us + C_os)

p = 6/(6 + 2.50)

p = 0.7058

p  = 70.58%

The z-score corresponding to 70.58% probability is approximately 0.54

Number of lettuce boxes = μ + (z*σ)

Number of lettuce boxes = 250 + (0.54*34)

Number of lettuce boxes = 250 + (18.36)

Number of lettuce boxes = 268.36

Number of lettuce boxes ≈ 268

Therefore, the supermarket should purchase 268 boxes of lettuce.

How to use z-table?

Step 1:

In the z-table, find the probability you are looking for and note down the two-digit number of the given row. (e.g 0.5, 2.2, 0.5 etc.)

Step 2:

Then look up at the top of z-table and note down the value in the column for the remaining decimal point in the range of 0.00 to 0.09.

Step 3:

Finally, add the numbers obtained from step 1 and step 2.

Find the perimeter of the circle is the same as finding the circumference of the circle.

Circumference Formula: C = 2πr

Divide the diameter by 2 to find the radius.

7 / 2 = 3.5

Solve using the given values.

C = 2(3.14)(3.5)

C = 2(10.99)

C = 21.98

Therefore, the circumference (perimeter) of the circle is 21.98cm²

Best of Luck!

Answer:

180

Step-by-step explanation:

12x15=180

Answer:

Step-by-step explanation:

x^-2 = (-3)^-2 = 1/(-3)^2 = 1/9

Each of the following is the previous value multiplied by -3,

x^-1 = x(x^-2) = (-3)(1/9) = -1/3

x^0 = x(x^-1) = (-3)(-1/3) = 1

x^1 = -3(1) = -3

x^2 = -3(-3) = 9

Answer:

Group A (distance in miles) 1, 1.5, 3.03, 3.2, 2.8, 1.5, 1.8, 2.5, 2.2) Group B (distance in miles) 2, 2.5, 3.23, 1.3, 1.8, 2.4, 3, 1.5, 1.8)Therefore, the correct answer is A) It is equal for Group A and Group B.

Answer:

3 units.

Step-by-step explanation:

We can calculate the length, since it only moves on the "x" axis, since on the "y" axis, it remains the same.

We know that between -2 to 5, there are 7 units. 2 + 5 = 7.

Therefore this would be the length.

We know that the perimeter is equal to:

p = 2 * w + 2 * l

P = 20

20 = 2 * w + 2 * 7

2 * w = 20 - 14

w = 6/2

w = 3

therefore, the width value is 3 units.

Answer:

3

Step-by-step explanation:

Answer:

  d.)  Arionna is incorrect. There are 27 cubic feet in a cubic yard because a cubic yard is a prism with dimensions 3 ft times 3 ft times 3 ft. A prism with those dimensions will take 27 cubes to fill it, if each cube is a unit cube of 1 ft³.

Step-by-step explanation:

There are (3 ft)(3 ft) = 9 ft² in one square yard. To find the volume of a cubic yard, you need to multiply that by 3 ft again: (9 ft²)(3 ft) = 27 ft³.

_____

Additional comment

For many problems involving units, I like to keep the units with the numbers. That helps ensure the math is done correctly. In this problem, simply multiplying ft by ft gives ft^2, not ft^3, so you know right away that you haven't computed volume correctly.

Answer:

y = [tex]-3x^2+12x-12[/tex]

Step-by-step explanation:

(x-2)^2 = (x-2)(x-2) => [tex]x^2-4x+4[/tex]

now, multiple every term by negative 3 and you get...

-3x^2+12x-12

Answer:

Step-by-step explanation:

Identify:      Hypothesized π = 0.22 n =1189 X = 230  

Estimate the sample proportion, p, of defective items. p= X/n = 230/1189 = 0.1934

List the formula for the standard error of a proportion.   [tex]\sqrt{PQ/n}[/tex]

Estimate the standard error of a proportion.  [tex]\sqrt{PQ/n} = \sqrt{0.22\times 0.78/1189} = 0.0120[/tex]

State the null and alternative hypotheses below.

H0: P = 0.22

H1: P<0.22

Illustrate the acceptance and rejection regions of the diagram to the right.

check the attached image below for the diagram

Identify the critical Z , -1.645

Fornulate the decision rule and list below.

If Z calculated is less than Z critical we reject null hypothesis

Calculate your test statistic.

[tex]Z= \frac{p-P}{\sqrt{PQ/n}} = \frac{0.1934-0.22}{0.0120}= -2.217[/tex]

Do you accept or reject the null hypothesis at 0.05 level of significance? Reject

State your conclusion. Should the quality control manage accept the shipment or return it?

WE have sufficient evidence that the population proportion of "like the ads a lot" for the company's ads is less than 0.22 at a 0.05 level of significance.

If a 0.01 level of significance had been used in the test, would you have accepted or rejected the null hypothesis?  

at 0.01 level of significance the critical value of Z is -2.33

Since Z calculated is greater than Z critical value we accept the null hypothesis

Answer:

Step-by-step explanation:

Answer:

$73.68

Step-by-step explanation:

2800 divide by 38 equals 73.68

Answer:

The hat was chosen was the child.

Step-by-step explanation:

Answer:

(a) We conclude that there is a significant association between prenatal exposure to antidepressant medicine and the risk of autism at 5% significance level.

(b) Yes, we can conclude that prenatal exposure to antidepressant medicine increases the risk of autism in the child.

Step-by-step explanation:

We are given that Autism and Maternal Antidepressant Use A recent study 41 compared 298 children with Autism Spectrum Disorder to 1507 randomly selected control children without the disorder.

Of the children with autism, 20 of the mothers had used antidepressant drugs. Of the control children, 50 of the mothers had used the drugs.

Let [tex]p_1[/tex] = proportion of mothers who had used drugs having Autism Spectrum Disorder in their children.

[tex]p_2[/tex] = proportion of mothers who had used drugs not having Autism Spectrum Disorder in their children.

(a) Null Hypothesis, [tex]H_0[/tex] : [tex]p_1=p_2[/tex]      {means that there is no significant association between prenatal exposure to antidepressant medicine and the risk of autism}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1\neq p_2[/tex]     {means that there is a significant association between prenatal exposure to antidepressant medicine and the risk of autism}

The test statistics that would be used here Two-sample z test 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 mothers who had used drugs having Autism Spectrum Disorder in their children = [tex]\frac{20}{298}[/tex] = 0.067

[tex]\hat p_2[/tex] = sample proportion of mothers who had used drugs not having Autism Spectrum Disorder in their children = [tex]\frac{50}{1507}[/tex] = 0.033

[tex]n_1[/tex] = sample of children with Autism Spectrum Disorder = 298

[tex]n_2[/tex] = sample of children without Autism Spectrum Disorder = 1507

So, the test statistics  =  [tex]\frac{(0.067-0.033)-(0)}{\sqrt{\frac{0.067(1-0.067)}{298}+\frac{0.033(1-0.033)}{1507} } }[/tex]

                                       =  2.281

The value of z test statistics is 2.281.

Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistic doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that there is a significant association between prenatal exposure to antidepressant medicine and the risk of autism.

(b) Yes, we can conclude that prenatal exposure to antidepressant medicine increases the risk of autism in the child because if we reconsider our hypothesis for one-tailed test in which the null hypothesis states that the prenatal exposure to antidepressant medicine does not increases the risk of autism in the child.

For this hypothesis also, our test statistics will be more than the critical value of z and due to which we reject our null hypothesis and conclude that prenatal exposure to antidepressant medicine increases the risk of autism.

The square root of 4 is 2. Since 3 is less than 4, the square root of 3 would be just under 2.

The first graph would be correct.

Answer:

The answer is ±0.5 or ±1/2

Step-by-step explanation:

When you solve by using the quadratic formula, you get double roots that will solve the equation. Hope this helps!!

The solution of the quadratic equation is 1/2 and 1/2.

We have to find, the solution of the quadratic equation is [tex]4x^2 + 3 = 4x + 2[/tex].

To determine the solution of the quadratic equation following all the steps given below.

Equation; [tex]4x^2 + 3 = 4x + 2[/tex]

        [tex]4x^2 + 3 = 4x + 2\\\\4x^2 + 3 - 4x - 2=0\\\\4x^2 -4x +1 =0[/tex]

                    [tex]\rm 4x^2-4x +1 = 0\\\\4x^2-2x -2x + 1= 0\\\\2x(2x-1) - 1 (2x-1)=0\\\\(2x-1) ( 2x-1) = 0[/tex]

                    [tex]\rm 2x- 1= 0 , \ 2x = 1 , \ x = \dfrac{1}{2}\\\\And \ 2x- 1= 0 , \ 2x = 1 , \ x = \dfrac{1}{2}\\\\[/tex]

Hence, The required solution of the equation is 1/2 and 1/2.

For more details refer to the link given below.

https://brainly.com/question/19776811

0.475

1000 milliliters is equal to 1 liter

Answer: 0.475 Liters

Step-by-step explanation: So, we know one liter is exactly 1,000 milliliters...therefore this would have to be a decimal.

Therefore, 475 milliliters to liters would be 0.475 liters.

Answer:

The second one.

Step-by-step explanation:

The others don't add up to that number

Answer:

As E is right angle , CD is hypotenuse , and ED is perpendicular and CE is the base .

Thus sinC = Perpendicular/ Hypotenuse

sinC = ED/CD

sinC = 3/5

The sine of an angle in a right triangle is the ratio of the side opposite to

the angle to the hypotenuse side.

Reasons:

The given parameters of ΔCDE are;

∠E = 90°, DC = 5, CE = 4, ED = 3

Required: The ratio that represents the sine of ∠C

Solution:

Given that ∠E = 90° therefore;

ΔCDE is a right triangle

DC = The hypotenuse side = 5

ED = 3 = The side opposite ∠C

[tex]sin\angle C = \mathbf{\dfrac{Opposite \ leg \ length}{Hypotenuse \ length}}[/tex]

Therefore;

[tex]\underline{sin\angle C \ is \ \dfrac{3}{5}}[/tex]

Learn more about trigonometric ratios here:

https://brainly.com/question/4232719

Answer:

In the Garden Club the cost will be a fixed fee of $25 and $10 for each rosebush, so if he buys X rosebushes, the total cost will be:

C1(X) = $25 + $10*X

While in the local nursery there is no initial cost, and each rosebush costs $15, so if he buys X rosebushes, the total cost will be:

C2(X) = $15*X

Now, let's find the value of X where C1 and C2 are equal, this is:

$25 + $10*X = $15*X

$25 = $15*X - $10*X = $5*X

X = 25/5 = 5

This means that if he buys 5 rosebushes, he will pay the same amount in both places.

If he buys less than 5 rosebushes, he will pay less in the local nursery (as it has a bigger slope, but no initial fee)

If he buys more than 5 rosebushes, he will pay less in the Garden club (because it has a smaller slope)