Estimate the difference.
141 - 5.89
8
O 12
O 16
O 20

Answer:

The probability is 0.2423.

Step-by-step explanation:

Given mean per capita = 19292 dollars

Given the variance = 540225

Now find the probability that the sample mean will be less than 19269 dollar when the sample is 499.

Below is the calculation:

[tex]\bar{X} \sim N(\mu =19292, \ \sigma = \frac{\sqrt{540225}}{\sqrt{499}}) \\\bar{X} \sim N(\mu =19292, \ \sigma = 32.90) \\\text{therefore the probability is:} \\P (\bar{X}< 19269) \\\text{Convert it to standard normal variable.} \\P(Z< \frac{19269-19292}{32.90}) \\P(Z< - 0.6990) \\\text{Now getting the probability from standard normal table}\\P(Z< -0.6990) = 0.2423[/tex]

Answer:

$180.20

Step-by-step explanation:

15% of $4800=$720

$4800-$720=$4080

6% of $4080=$244.8

$4080+$244.8=$4,324.80

$4,324.80/24=$180.20

so you would pay $180.20 a month

Answer:

it is c

Step-by-step explanation:

i did it myself like a man. (this is for edgenutiy 2020)

The inequality representing the possible price of each DVD is P < 12.50

A relationship between two expressions or values that are not equal to each other is called inequality.

Given that, Nikki had a $50 gift card for her favorite store. She used the gift card to buy 4 DVDs and still had money available on the card after the purchase, the DVDs were all the same price,

We need to find the possible price of each DVD,

Since, the maximum amount in the card is $50, after buying 4 DVDs there is still money available on the card,

Therefore, the maximum possible price of one DVD can be $50/4 = $12.5

But there is still money available on the card, that means the price of the DVD is less than $12.5

If p be the price of the one DVD, then,

p < 12.50

Hence, the inequality representing the possible price of each DVD is P < 12.50

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Answer:

B.

Step-by-step explanation:

"negative reciprocal slopes" means the lines are perpendicular, so they will always intersect.

Hence there will be exactly one solution.

B. The system will have one solution.

The slopes of perpendicular strains, or bisecting strains, are continually terrible reciprocals of each other. For instance, if the slope of a line is -five, then the slope of a line perpendicular to this line will be the negative reciprocal of -five.

If the 2 traces have exclusive slopes, then they'll intersect as soon as. consequently, the gadget of equations has exactly one answer. If the two traces have the equal slope however of kind y-intercepts, then they're parallel strains, and they'll by no means intersect.

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Anwer:3.537m

STEP BY STEP EXPLANATIOND:using SOH CAH TOA

First find the opposite

Represent the opposite with x

Tan 33° =x\10

x=10Tan 33°

x=6.494

To find m

Sin 33°=m\6.494 Sin 33°

m=3.5368

m=3.537meteres

Answer

260 kilograms

Step-by-step explanation:

the correct answer is 260 kg

Answer: 12.6 kg

Step-by-step explanation: add the amounts of food for her farm, and just search for how many kg are in 1,260 grams

Answer:

Option (C)

Step-by-step explanation:

Since FJ is the bisector of AD,

AL ≅ DL

And it's given that BL ≅ LC

Length of BL is 10 less than the length of AB.

m(BL) = m(AB) - 10

m(AD) = 220 [Since m(AD) = 2m(AL)]

2m(AL) = 220

m(AL) = 110

m(AB) + m(BL) = 110

m(AB) + [m(AB) - 10] = 110

2m(AB) = 110 + 10

m(AB) = 60

Therefore, m(BL) = m(AL) - m(AB)

                            = 110 - 60

                            = 50

Since, m(AL) = m(DL)

m(AB) + m(BL) = m(LC) + m(CD) [Since BL = LC]

m(AB) = m(CD) = 60

Now m(BD) = m(BL) + m(LC) + m(CD)

                   = 50 + 50 + 60

                   = 160

Therefore, option (C) will be the answer.

Answer:

The equation that describes the function is y = -6x-1

Step-by-step explanation:

Firstly we can see that the graph passes through the origin.

The general equation of a starlight line graph is;

y = mx + c

where m is the slope and c is the y-intercept

what’s left now is go find our slope

We need two points for this on the line.

Let’s identify these points;

The identifiable points are; (1,-7) and (-1,5)

So the formula for the slope is;

y2-y1/x2-x1 = (5-(-7))/(-1-1) = 12/-2 = -6

Thus, the equation of the line becomes

y = -6x + c

Looking at the graph again, we can see an obvious y-intercept at the point y = -1

So our intercept is -1

The equation of the line is thus;

y = -6x -1

Answer:

105.86 grams of AuCl3, if the compound has 6.3 x10^23 atoms of Cl.

Step-by-step explanation:

We are given that the compound has 6.3 x10^23 atoms of Cl.

To find how many molecules of AuCl3 are in the given compound, we divide the compound by 3, i.e;

[tex]\frac{6.3 \times 10^{23} }{3}[/tex]  =  [tex]2.1\times 10^{23}[/tex] molecules of AuCl3.

Now, as we know that 1 mole of AuCI3 has [tex]6.022 \times 10^{23}[/tex] molecules.

So, the moles that our compound has is given by;

      =  [tex]\frac{2.1 \times 10^{23} }{6.022 \times 10^{23} }[/tex]  = [tex]\frac{2.1}{6.022}[/tex]  = 0.349 mole AuCI3

Also, the molar mass of AuCI3 = 303.33 g/mole

So, the molar mass of 0.349 moles AuCI3 =  [tex]303.33 \times 0.349[/tex]

                                                                      =  105.86 g

Hence, 105.86 grams of AuCl3, if the compound has 6.3 x10^23 atoms of Cl.

Answer:

P=20

Step-by-step explanation:

first find the distance between the points:

AB, BC,CD and DA

A(2,-3) , B(4,-3) , C(4,5) , D (2,5)

distance d= √(x2-x1)^2+(y2-y1)^2

for AB= d= √(4-2)^2+(-3-(-3))^2

AB=2

same thing for the rest of the lines

BC=√(4-4)^2+(5-(-3))^2

BC=8

CD=2

DA=8

perimeter=8+8+2+2=20

Answer: 7 packages

Step-by-step explanation:

From the question, we are told that a truck is to be filled with packages that weigh 5.8kg. The maximum capacity of the truck is 48000 grams(48kg) and there is a 5500 gram(5.5kg) package already in the truck.

First, we need to subtract 5.5kg from 48kg to know the amount of space left. This will be:

= 48kg - 5.5kg

= 42.5kg

To get the number of 5.8kg packages that can be loaded, we divide 42.5kg by 5.8kg. This will be:

= 42.5kg/5.8kg

= 7.3

= 7 approximately

Therefore, 7 packages will be loaded.

N.B: 1000 grams = 1 kilogram

Answer:

The coefficients are;

1,28,378 and 3,276

Step-by-step explanation:

For the binomial expansion, when we talk of the coefficients, we mean the whole numbers that stands before the alphabets

For example, the coefficient of x in 2x is 2

Back to the question;

(x + y)^28

= 28C0 x^28y^0 + 28C1 X^27y^1 + 28C2 x^26y^2 + 28C3 x^25y^3 + ..........

So the coefficients we are looking for are;

28C0 = 1

28C1 = 28

28C2 = 378

28C3 = 3,276

Kindly note that 28C0 is read as 28 combination zero and so on

Answer:

11/60

Step-by-step explanation:

hello

in total there are 120 ppl

22 are vanilla cones

so the probability that this person bought a vanilla a ice cream cone is 22/120=11/60

hope this helps

Answer:

The Museum is 7 blocks south and 3 blocks east

Step-by-step explanation:

Since from the hotel Ruby went 1 block west (left) during the whole time traveled, you would go 3 east (from hotel to museum).

Then in total Ruby went south 7 blocks.

Answer:  [tex]a)\ \text{Vertex}:y=-\dfrac{3}{2}(x+1)^2+6[/tex]

                [tex]b)\ \text{Standard}:y=-\dfrac{3}{2}x^2-3x=\dfrac{9}{2}[/tex]

              c) Transformations: reflection over the x-axis,

                                               vertical stretch by a factor of 3/2,

                                               horizontal shift 1 unit to the left,

                                               vertical shift 6 units up

Step-by-step explanation:

Intercept form: y = a(x - p)(x - q)

Vertex form: y = a(x - h)² + k

Standard form: y = ax² + bx + c

We can see that the new vertex is (-1, 6). Use the Intercept form to find the vertical stretch: y = a(x - p)(x - q) where p, q are the intercepts.

p = -3, q = 1, (x, y) = (-1, 6)

a(-1 + 3)(-1 -1) = 6

       a (2)(-2) = 6

                a  = -6/4

                 a = -3/2

a) Input a = -3/2 and vertex (h, k) = (-1, 6) into the Vertex form to get:

[tex]y=-\dfrac{3}{2}(x+1)^2+6[/tex]

b) Input a = -3/2 into the Intercept form and expand to get the Standard form:

[tex]y=-\dfrac{3}{2}(x+3)(x-1)\\\\\\y=-\dfrac{3}{2}(x^2+2x-3)\\\\\\y=-\dfrac{3}{2}x^2-3x+\dfrac{9}{2}[/tex]

c) Use the Vertex form to identify the transformations:

[tex]y=-\dfrac{3}{2}(x+1)^2+6[/tex]

Answer:

y = -[tex]\frac{2}{5}[/tex]x - 1

Step-by-step explanation:

First, we can put the equation into y = mx + b form:

2x + 5y = 10

5y = -2x + 10

y = -[tex]\frac{2}{5}[/tex]x + 2

Now, we know the slope is -[tex]\frac{2}{5}[/tex]. A parallel line will have the same slope.

So, we can plug in the point (-5, 1) into the equation y = -[tex]\frac{2}{5}[/tex]x + b to find b:

1 = -[tex]\frac{2}{5}[/tex](-5) + b

1 = 2 + b

-1 = b

So, the equation will be y = -[tex]\frac{2}{5}[/tex]x - 1

Hey there! :)

Answer:

a. b = y - mx

b. x = y - b /m

c. t = I/ pr

d. t = A - p/pr

Step-by-step explanation:

a. y = mx + b (for b)

Isolate the b variable by subtracting both sides by mx:

y - mx = b.

Therefore:

b = y - mx.

b. y = mx + b (for x)

Subtract 'b' from both sides:

y - b = mx

Divide 'm' from both sides:

y - b / m = x

c. I = prt

Divide both sides by pr:

I /pr = t.

d. A = p + prt

Subtract p from both sides:

A - p = prt

Divide both sides by pr:

A - p / pr = t

Answer:

151515 not found

Step-by-step explanation:

For every 555 nuts found, 333 are not.  This gives a total of 888.

555 + 333 = 888

Divide the total number of nuts by this number.

404040/888 = 455

Multiply the number that get found and the number that don't by the number calculated above.

555 × 455 = 252525

333 × 455 = 151515

252525 nuts will be found and 151515 will not.

Answer:

15

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

Original dimensions:

L = x

W = x

Now we reduce the width by 2 ft and increase the length by 2 ft.

L = x + 2

W = x - 2

The area is the product of the length and width.

A = LW = (x + 2)(x - 2)

The original length and width are 10 ft.

L = W = x = 10

A = LW = (10 + 2)(10 - 2) = 12 * 8 = 96

The new area is 96 sq ft.

Answer: D.

Answer:

Solution,

Base ( BC ) = 22 cm

Perpendicular ( AC) = 8 cm

Hypotenuse (AB) = ?

Now,

Using the Pythagoras theorem:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

[tex] {h}^{2} = {(8)}^{2} + {(22)}^{2} [/tex]

[tex] {h}^{2} = 64 + 484[/tex]

[tex] {h}^{2} = 548[/tex]

[tex]h = \sqrt{548} [/tex]

[tex]h = 23.40 \: cm[/tex]

Hope this helps..

Good luck on your assignment...

Answer:

D. the exponent can be odd

Step-by-step explanation:

A. (-4)² = 16 ⇒ -4 is even and the product is positive.

B. (-5)² = 25 ⇒ -5 is odd and the product is positive.

C. (-5)⁴ = 625 ⇒ The exponent 4 is even and the product is positive.

D. (-5)⁵ = -3125 ⇒ The exponent 5 is odd and the product is negative.

So, the answer is D.

Hope this helps.

Answer:

It's described in the explanation

Step-by-step explanation:

Your picture only shows one number line that isn't correct.

The number line that is correct has a filled in dot and is pointing to the left.

The dot is filled in because the inequality is less than or equal to

Since it is less than, the arrow points to the left

Answer:

Well you only have one number line but I can tell you that if x is less than or equal to 0 then it will be a closed filled in dot that is on the number 0 and is going left because x is less than or equal to 0.

So it will look something like this. Look at the image below.

Answer:

36° and 54°

Step-by-step explanation:

Complementary angles are angles whose sum equals to 90°

Hence C +D = 90°

The ratio of C &D = 2:3 respectively

Sum of the ratio = 2+3 = 5

Hence we divide each of the ratio by the sum of the entire ratio and then multiply by 90°

For angle C :

2/5 × 90

2×18 = 36°

For angle D :

3/5× 90

3×18 = 54°

Hence the angles are 36° and 54° respectively

To proof that we are actually right

C+D = 90°

36+54 = 90°

Hence the answer is right.

Answer:

(B)3 seconds.

Step-by-step explanation:

The object will be on the ground when its height is zero.

Therefore given the height function:

[tex]h(t)=144-16t^2\\$When h(t)=0\\144-16t^2=0\\16t^2=144\\$Divide both sides by 16\\t^2=9\\t=3$ sec[/tex]

The object will be on the ground afyer 3 seconds.

It will take 3 seconds for the object to reach the ground from a height of h(t) = 144 - 16t²

Word problems involving the use of algebraic expression require a good step-by-step interpretation with the use of variables to effectively solve the problem and arrive at a valid answer.

From the given information:

The height of an object that is allowed to drop from freefall to the ground is:

At the time when h(t) = 0

0 = 144 - 16t²

16t² = 144

t² = 144/16

t² = 9

t = √9

t = 3 seconds

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Answer:

1/17 0r 6%

Step-by-step explanation:

the answer is rounded up for you

Answer:

The new dimensions are 6.18 cm by 16.18 cm.

Step-by-step explanation:

Original dimensions were 30 cm by 20 cm.

We decrease length and width by x and calculate the area:

Area = (length)(width)

        = (30 - x)(20 - x) = 100

Performing the indicated multiplication, we get:

600 - 30x - 20x + x^2 = 100, or, after simplification,

x^2 - 50x + 500 = 0

Let's solve this by completing the square:

x^2 - 50x + 500 = x^2 - 50x + 625 - 625 + 500 = 0

This simplifies to (x - 25)^2 - 125 = 0, or (x - 25)^2 = 125

Taking the square root of both sides, we get:

x - 25 = ±√125, or

x = 25 ± 5√5

The two results are x = 36.18 (not possible, because we DECREASED the original dimensions) and x = 13.82 (possible)

The dimensions of the new rectangle are

(30 - 13.82) cm by (20 - 13.82) cm, or

16.2 cm by 6.18 cm

Check:  With these dimensions is the area 100 cm^2, as expected?

(6.18)(16.18) = 99.9979    YES

Answer:

Step-by-step explanation:

This problem bothers on the conversion of units

to get the scale we need to know how many millimetres are there in one km.

Hence the scale is 1,000,000 mm:1 km