A gift box shown below is packed with small cubic 1/2 inch blocks. The blocks are packed tightly with no spaces between them.
A. How many blocks are in the gift box?
B. What is the volume of the gift box?
C. Find how much wrapping paper will be needed to wrap the gift box (hint: find surface area).

The equation has 2 valid solutions; no extraneous solutions

The given equation is:

[tex]\sqrt{x - 1} - 5= x - 8[/tex]

First, we determine the solutions

[tex]\sqrt{x - 1} - 5= x - 8[/tex]

Add 5 to both sides

[tex]\sqrt{x - 1} = x - 8 + 5[/tex]

[tex]\sqrt{x - 1} = x - 3[/tex]

Square both sides

[tex]x - 1 = (x - 3)^2[/tex]

Expand

[tex]x - 1 = x^2- 3x - 3x + 9[/tex]

[tex]x - 1 = x^2- 6x + 9[/tex]

Collect like terms

[tex]x^2 - 6x - x + 9 + 1 = 0[/tex]

[tex]x^2 - 7x + 10 = 0[/tex]

Expand again

[tex]x^2 - 2x-5x + 10 = 0[/tex]

Factorize

[tex]x(x - 2) -5(x -2)= 0[/tex]

Factor out x - 2

[tex](x - 5)(x -2)= 0[/tex]

Split

[tex]x - 5=0[/tex] or [tex]x - 2 = 0[/tex]

[tex]x= 5[/tex] or [tex]x = 2[/tex]

The above values are valid values of x.

Hence, the equation has 2 valid solutions; no extraneous solutions

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Answer:

That person is wrong, First blank is : one valid solution , Second blank is : one extraneous solution, and I'm not sure what the 3rd blank is but I think It's 4.

Step-by-step explanation:

for plato users

I believe the question is:

What is the solution to 5x + 1 +9 - 3

In this case, we solve for X.

5x + 1 + 9 - 3

5x + 10 - 3

5x + 7

5x = -7

x = -7/5

Unfortunately, It is not one of the answer choices it looks like.

Maybe you should reword your question but hopefully this is correct.

If you meant to say 5x+1 + 9 < 3 --> 5x + 10 < 3 --> 5x < -7 --> x < -7/5

The value of x in a given expression is -7/5.

We have given that,

5x + 1 + 9 - 3

We have to determine the value of x.

A variable is any factor, trait, or condition that can exist in differing amounts or types. Scientists try to figure out how the natural world works

In this case, we solve for X.

5x + 1 + 9 - 3

5x + 10 - 3

5x + 7

5x = -7

x = -7/5

If you meant to say 5x+1 + 9 < 3 --> 5x + 10 < 3 --> 5x < -7 --> x < -7/5.

Therefore we get the value of x is -7/5.

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Answer:

B

Step-by-step explanation:

Since we know the measure of ∠B and the side opposite to ∠B and we want to find BC, which is adjacent to ∠B, we can use the tangent ratio. Recall that:

[tex]\displaystyle \tan\theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]

The angle is 54°, the opposite side measures 16 units, and the adjacent side is BC. Substitute:

[tex]\displaystyle \tan 54^\circ = \frac{16}{BC}[/tex]

Solve for BC. We can take the reciprocal of both sides:

[tex]\displaystyle \frac{1}{\tan 54^\circ} = \frac{BC}{16}[/tex]

Multiply:

[tex]\displaystyle BC = \frac{16}{\tan 54^\circ}[/tex]

Use a calculator. Hence:

[tex]\displaystyle BC \approx 11 .62\text{ units}[/tex]

BC measures approximately 11.62 units.

Our answer is B.

Answer:

The answer is "Specific treatment levels".

Step-by-step explanation:

When we experimenting with 'level' which is related to the quantity or magnitude of treatment. For this part of an experiment or study, a group or individual is exposed to a specified set of circumstances. For example: If four categories are exposed to different doses of a given drug, then each dose reflects a level of a treatment factor in the model.

Answer:

C

Step-by-step explanation:

Just trust

Answer:

C

Step-by-step explanation:

I did the assignment in edge and got it right.

Proof:

Answer:

b=120°

c=60°

d=60°

SEE THE IMAGE FOR SOLUTION

Work Shown:

30 min = 30/60 = 0.5 hours

distance = rate*time

rate = distance/time

rate = (2450 miles)/(0.5 hours)

rate = (2450/0.5) mph

rate = 4900 mph

For the sake of comparison, a typical commercial passenger jet can reach max speeds of about 600 mph.

Answer:

U = 67.6 degrees

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos U = adj side / hypotenuse

cos U = sqrt(10)/ sqrt(69)

cos U = sqrt(10/69)

Taking the inverse cos of each side

cos ^-1( cos U) =  cos ^-1(sqrt(10/69))

U = 67.62335

To the nearest tenth

U = 67.6 degrees

Step-by-step explanation:

here's the answer to your question

Answer:

-2pi/3

Step-by-step explanation:

y = 2 cos 3(x + 2π∕3) +1

y = A sin(B(x + C)) + D  

amplitude is A

period is 2π/B

phase shift is C (positive is to the left)

vertical shift is D

We have a shift to the left of 2 pi /3

Answer:

A

Step-by-step explanation:

The standard cosine function has the form:

[tex]\displaystyle y = a\cos (b(x-c)) + d[/tex]

Where |a| is the amplitude, 2π / b is the period, c is the phase shift, and d is the vertical shift.

We have the function:

[tex]\displaystyle y = 2 \cos 3\left(x + \frac{2\pi}{3}\right) + 1[/tex]

We can rewrite this as:

[tex]\displaystyle y = \left(2\right)\cos 3\left(x - \left(-\frac{2\pi}{3}\right)\right) + 1[/tex]

Therefore, a = 2, b = 3, c = -2π/3, and d = 1.

Our phase shift is represented by c. Thus, the phase shift is -2π/3.

Our answer is A.

the answer is

10² ( ten square )

step by step :

10² = 10 × 10

= 100

Answer: 100

Step-by-step explanation: 10*10=100

Answer:

stundeez

Step-by-step explanation:

Nicki Minaj hdhsbskdhsnsk

Answer:

The function to determine the value of your car (in dollars) in terms of the number of years t since 2012 is:

[tex]f(t) = 10000(0.9407)^t[/tex]

Step-by-step explanation:

Value of the car:

Constant rate of change, so the value of the car in t years after 2012 is given by:

[tex]f(t) = f(0)(1-r)^t[/tex]

In which f(0) is the initial value and r is the decay rate, as a decimal.

In 2012 your car was worth $10,000.

This means that [tex]f(0) = 10000[/tex], thus:

[tex]f(t) = 10000(1-r)^t[/tex]

2014 your car was worth $8,850.

2014 - 2012 = 2, so:

[tex]f(2) = 8850[/tex]

We use this to find 1 - r.

[tex]f(t) = 10000(1-r)^t[/tex]

[tex]8850 = 10000(1-r)^2[/tex]

[tex](1-r)^2 = \frac{8850}{10000}[/tex]

[tex](1-r)^2 = 0.885[/tex]

[tex]\sqrt{(1-r)^2} = \sqrt{0.885}[/tex]

[tex]1 - r = 0.9407[/tex]

Thus

[tex]f(t) = 10000(1-r)^t[/tex]

[tex]f(t) = 10000(0.9407)^t[/tex]

Solution :

Given data :

20.1     33.5     21.7      58.4     23.2     110.8     30.9

24.0    74.8     60.0

n = 10

Range : Arranging from lowest to highest.

20.1,   21.7,   23.2,    24.0,   30.9,    33.5,    58.4,    60.0,    74.8,   110.8

Range = low highest value - lowest value

           = 110.8 - 20.1

           = 90.7

Mean = [tex]$\frac{\sum x}{n}$[/tex]

         [tex]$=\frac{20.1+21.7+23.2+24.0+30.9+33.5+58.4+60.0+74.8+110.8}{10}$[/tex]

          [tex]$=\frac{457.4}{10}$[/tex]

         [tex]$=45.74$[/tex]

Sample standard deviation :

[tex]$S=\sqrt{\frac{1}{n-1}\sum(x-\mu)^2}$[/tex]

[tex]$S=\sqrt{\frac{1}{10-1}(20.1-45.74)^2+(21.7-45.74)^2+(23.2-45.74)^2+(24.0-45.74)^2+(30.9-45)^2}$[/tex]  

      [tex]\sqrt{(33.5-45.74)^2+(58.4-45.74)^2+(60.0-45.74)^2+(74.8-45.74)^2+(110.8-45.74)^2}[/tex]

[tex]$S=\sqrt{\frac{1}{9}(657.4+577.9+508.0+472.6+220.2+149.8+160.2+203.3+844.4+4232.8)}$[/tex][tex]$S=\sqrt{\frac{1}{9}(8026.96)}$[/tex]

[tex]$S=\sqrt{891.88}$[/tex]

S = 29.8644

Variance = [tex]S^2[/tex]

               [tex]=(29.8644)^2[/tex]

               = 891.8823

Answer:

a. 3/4 of pocket money left

b. R10

Step-by-step explanation:

a. 4/4 - 1/4 = 3/4

b. 40/4 = 10 = 1/4 of pocket money

(a). The fraction of pocket money left is 3/4

(b). If he had R40 pocket money, he spend R10.

The ratio is defined as a relationship between two quantities, it is expressed one divided by the other.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

The operator that perform arithmetic operation are called arithmetic operators .

Operators which let do basic mathematical calculation

+ Addition operation : Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation : Subtracts right hand operand from left hand operand.

for example 4 -2 = 2

* Multiplication operation : Multiplies values on either side of the operator

For example 4*2 = 8

Mandla spent one-quarter of his pocket money on sweets

Let x be the total amount of pocket money Mandla had originally

Solution of (a).

⇒ x - (1/4)x

⇒ (3/4)x

The fraction of pocket money left = 3/4

Solution of (b).

1/4 of pocket money

⇒ (1/4)x

⇒ (1/4)40

⇒ 10

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Answer:

C. rotation 180º about the origin

Step-by-step explanation:

Given

Quadrilaterals GWVY and G'W'V'Y'

Required

Describe the transformation rule

Pick points Y and Y'

[tex]Y = (5,-4)[/tex]

[tex]Y' = (-5,4)[/tex]

The above obeys the following rule:

[tex](x,y) \to (-x,-y)[/tex]

When a point is rotated by 180 degrees, the rule is:

[tex](x,y) \to (-x,-y)[/tex]

Hence, (c) is correct

opposite angles are equal

[tex]\\ \sf\longmapsto 13x+19=84[/tex]

[tex]\\ \sf\longmapsto 13x=84-19[/tex]

[tex]\\ \sf\longmapsto 13x=65[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{65}{13}[/tex]

[tex]\\ \sf\longmapsto x=5[/tex]

Answer:

[tex]\boxed {\boxed {\sf x=5}}[/tex]

Step-by-step explanation:

We are asked to solve for x.

We are given a pair of intersecting lines and 2 angles measuring (13x+19)° and 84°. The angles are opposite each other, so they are vertical angles. This means they are congruent or have the same angle measure.

Since the 2 angles are congruent, we can set them equal to each other.

[tex](13x+19)=84[/tex]

Solve for x by isolating the variable. This is done by performing inverse operations.

19 is being added to 13x. The inverse operation of addition is subtraction. Subtract 19 from both sides of the equation.

[tex]13x+19-19= 84 -19[/tex]

[tex]13x= 84 -19[/tex]

[tex]13x=65[/tex]

x is being multiplied by 13. The inverse operation of multiplication is division. Divide both sides by 13.

[tex]\frac {13x}{13}= \frac{65}{13}[/tex]

[tex]x= \frac{65}{13}[/tex]

[tex]x= 5[/tex]

For this pair of vertical angles, x is equal to 5.

9514 1404 393

Answer:

  $3277.23

Step-by-step explanation:

The future value of the CD with interest at rate r compounded semiannually for t years will be given by ...

  A = P(1 +r/2)^(2t)

where P is the principal value.

For the given rate and time, this is ...

  A = $2000(1 +0.05/2)^(2·10) = $2000(1.025^20) ≈ $3277.23

The value of the CD at maturity will be $3277.23.

Answer:

The p-value of the test is 0.4414, higher than the standard significance level of 0.05, which means that there is not a a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees.

Step-by-step explanation:

Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.

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]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Apartment:

38 out of 78, so:

[tex]p_A = \frac{38}{78} = 0.4872[/tex]

[tex]s_A = \sqrt{\frac{0.4872*0.5128}{78}} = 0.0566[/tex]

Home:

46 out of 84, so:

[tex]p_H = \frac{46}{84} = 0.5476[/tex]

[tex]s_H = \sqrt{\frac{0.5476*0.4524}{84}} = 0.0543[/tex]

Test if the there a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees:

At the null hypothesis, we test if there is no difference, that is, the subtraction of the proportions is equal to 0, so:

[tex]H_0: p_A - p_H = 0[/tex]

At the alternative hypothesis, we test if there is a difference, that is, the subtraction of the proportions is different of 0, so:

[tex]H_1: p_A - p_H \neq 0[/tex]

The test statistic is:

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

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the samples:

[tex]X = p_A - p_H = 0.4872 - 0.5476 = -0.0604[/tex]

[tex]s = \sqrt{s_A^2 + s_H^2} = \sqrt{0.0566^2 + 0.0543^2} = 0.0784[/tex]

Value of the test statistic:

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

[tex]z = \frac{-0.0604 - 0}{0.0784}[/tex]

[tex]z = -0.77[/tex]

P-value of the test and decision:

The p-value of the test is the probability of the difference being of at least 0.0604, to either side, plus or minus, which is P(|z| > 0.77), given by 2 multiplied by the p-value of z = -0.77.

Looking at the z-table, z = -0.77 has a p-value of 0.2207.

2*0.2207 = 0.4414

The p-value of the test is 0.4414, higher than the standard significance level of 0.05, which means that there is not a a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees.

Answer:

Since the triangle is a right angled triangle, one of the angles is 90°. In the right angled triangle, the acute angles are in the ratio 4:5. Let the measures of the acute angles of the triangle in degrees be 4k and 5k, where k is a constant.

Step-by-step explanation:

hope it helps.

Answer:

40and50

Step-by-step explanation:

let the acute angles be 4x and 5x then,

4x+5x+90=180 [sum of all angles of a right angled triangle]

or,9x=180-90

or,x=90/9

x=10

4x=4×10=40

5x=5×10=50

Answer:

D) a = - 5/2

Step-by-step explanation:

2x -5y - 7 = 0

5y = 2x - 7

y = 2/5 x - 7

the slope of this line is therefore 2/5 (factor of x).

the perpendicular slope is then (exchange y and x and flip the sign) -5/2, which is then a and the factor of x.

Answer:

The new price is 66% off the original not 75% off

Step-by-step explanation:

Let x be the original price

First take 60 percent off

x - x*60% = new price

x- .60x = .40x

The new price is .40x

Then take 15 % off

(.40x) - (.40x)*15%

.40x - .40x*.15

.40x - .06x

.34x

100 -.34 =.66

The new price is 66% off the original not 75% off

Answer:

9

Step-by-step explanation:

it's as simple as that 9 is 9 away from 0

Answer:

Option (A)

Step-by-step explanation:

Solution of two functions represented by the graph are the common points or point of intersection of the graphs.

From the graph attached,

Parabola and ellipse are intersecting each other at four points.

Therefore, solutions of the given non linear functions will be FOUR.

Option (A) will be the correct option.

Answer:

Step-by-step explanation:

Answer:

12.6 ft

Step-by-step explanation:

Answer:

hope it helps you..........

Answer:

60

Step-by-step explanation:

g(x)= x^2 +8x - 24

Substitute x for 6 in the equation

g(6)= 6^2 + 8(6) - 24

= 36+48-24

= 60

Answer:

c. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.32 and 39.68.

Step-by-step explanation:

Given :

Groups:

x1 = 69 ; s1 = 19 ; n1 = 38

x2 = 32 ; s2 = 14 ; n2 = 37

1 - α = 1 - 0.95 = 0.05

Using a confidence interval calculator to save computation time, kindly plug the values into the calculator :

The confidence interval obtained is :

(24.32 ; 39.68) ; This means that we are 95% confident that the true mean difference in ALT values between the two population lies between

(24.32 ; 39.68) .

The odd natural number x such that the LCM of x and 40 is 1400 is 35

The least common multiple the lowest multiple of two or more numbers.

From the question, we need to determine the value of x of the LCM of the numbers is 1400

LCM (x,40) = 1400

Find a possible value of x

x = 1400/40

x = 35

Hence the odd natural number x such that the LCM of x and 40 is 1400 is 35

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