Show that (2.1) is a solution of the system of equations.
Substitute (2, 1) into x + 3y = 5 to get -
Simplify the equation to get -
Substitute (2, 1) into y = -x+ 3 to get -
Simplify the equation to get -

Answer:

A - 9/34

B - 7/34

Step-by-step explanation:

A girl grabs a lollipop - 9/34 (Event A)

A boy grabs a fruit chew - 7/34 (Event B)

Because there are 34 possibilities in total....

Thanks!

Answer:

11.2467

Step-by-step explanation:

First we need to find the mean

Add up all the data and divide by number of points)

(6+7+8+10+12+13+14+17+17+17+18+19+21+23+24+24+25+27+31+31+32+36+36+39+41+45+45+46+49+50)/30

261/10

26.1

Then to find the mean absolute deviation take each value and find the absolute value from the mean and sum it and then divide by the number of points

((26.1 -6)+(26.1-7)+(26.1-8)+(26.1-10)+(26.1-12)+(26.1-13)+(26.1-14)+(26.1-17)+(26.1-17)+(26.1-17)+(26.1-18)+(26.1-19)+(26.1-21)+(26.1-23)+(26.1-24)+(26.1-24)+(26.1-25)+(27-26.1)+(31-26.1)+(31-26.1)+(32-26.1)+(36-26.1)+(36-26.1)+(39-26.1)+(41-26.1)+(45-26.1)+(45-26.1)+(46-26.1)+(49-26.1)+(50-26.1))/30

11.2467

Answer:

11 16/75

Step-by-step explanation:

Find the mean: sum/n

783/30

26.1

Find individual |x - 26.1| and add them:

|6-26.1| + |7-26.1| + ...... + |50-26.1|

= 20.1 + 19.1 + .... + 23.9

= 336.4

M.A.D = 336.4/30

11 16/75

Answer:

$45-$2.50xx

Step-by-step explanation:

Let first of all determine the original amount on the gift card as follows

amount utilized=$2.50*16=$40

balance left after utilizing $40=$5

original amount on the gift card=amount utilized+balance left=$40+$5=$45

if xx cups of coffee is purchased ,the amount utilized would be xx*$2.50

i.e $2.50xx

The equation for the amount left would total amount on the gift card minus the $2.50xx

equation for amount remaining =$45-$2.50xx

If the questioner has duplicated x,which means he or she meant just x

equation of the amount remaining would=$45-$2.50x

Answer:

D

Step-by-step explanation:

each angle of the triangle is 95° and the second angle has to be in alphabetical order

The true statement is ∠BAC + ∠ABC = 95°

An angle is a figure formed by two rays or lines that share a common endpoint, called the vertex.

Angles can lie in a plane or be formed by the intersection of two planes or two curves. A reflex angle is an angle that is greater than 180 degrees but less than 360 degrees.

Given is a figure, we need to find the correct answer from the option,

We know that,

The sum of two opposite interior angles of a triangle is equal to the measurement of the exterior angle.

Therefore,

∠BAC + ∠ABC = ∠ACD

∠BAC + ∠ABC = 95°

Hence, the true statement is ∠BAC + ∠ABC = 95°

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Answer:

Step-by-step explanation:

We need to explain the transformations applied to 1/x to get f(x). We get f by following the following steps.

1. Multiply 1/x by 200 to get the function 200/x. This represents taking the graph of 1/x and expanding it vertically by a factor of 200.

2. Sum 10 units to 200/x. This represents a vertical shift of 10 units to the graph of 200/x.

Answer:

2.86cm

Step-by-step explanation:

Step 1:

Data obtained from the question. This includes the following:

Volume (V) = 187cm3

Height (h) = 7.3cm

Pi (π) = 3.14

Radius (r) =..?

Step 2:

Determination of the radius of the cylindrical water bottle.

The radius of the cylindrical water bottle can be obtained as follow:

V = πr^2h

187 = 3.14 x r^2 x 7.3

Divide both side by 3.14 x 7.3

r^2 = 187 / (3.14 x 7.3)

Take the square root of both side

r = √[187 / (3.14 x 7.3)]

r = 2.86cm

Therefore, the radius of the cylindrical water bottle is 2.86cm

Answer:

y=x-4

Step-by-step explanation:

The general scaffold for the slope intercept form is y=mx+b, where m is the slope and b is the y intercept. You can rearrange the equation that you are given like this:

2x-2y=8

-2y=-2x+8

y=x-4

Hope this helps!

Answer:

Rearrange the equation so that it is written in slope intercept form:

y=mx+b.

2x+2y=8.

2y=−2x+8.

y=−x+4.

Answer:

Step-by-step explanation:

1 negative x-tile and 8 positive unit tiles on the left side; 7 positive x-tiles and 8 negative unit tiles on the right side

Answer:

the answer is c

Step-by-step explanation:

Answer:

48^2 =2304 < 2345 < 2401 = 49^2

=> Smallest number should be: 2401 - 2345 = 56

Hope this helps!

:)

Answer:

56

Step-by-step explanation:

sqrt(2345) = 48.425...

Nearest integer is 49

So, the nearest perfect is 49²

49² = 2401

To be added:

2401 - 2345

56

Answer:

x = -3/2          x=2

Step-by-step explanation:

2x² - x-6=0

Factor

(2x     ) (x      ) =0

6 = 2*3

2*-2 +3 = -1

(2x  +3   ) (x  -2    ) =0

2x+3 =0      x-2 =0

2x = -3            x=2

x = -3/2          x=2

Answer:

[tex]r = 16[/tex], [tex]s = -48[/tex]

Step-by-step explanation:

The values of [tex]r[/tex] and [tex]s[/tex] can be found with the help of algebraic manipulation on the second-order polynomial described on statement:

[tex]f(x) = 3\cdot x^{2} - 24\cdot x + \frac{1}{3}[/tex]

[tex]f(x) = 3\cdot (x^{2} - 8\cdot x) + \frac{1}{3}[/tex]

[tex]f(x) = 3\cdot (x^{2} - 8\cdot x + 16 - 16) + \frac{1}{3}[/tex]

[tex]f(x) = 3\cdot (x^{2}-8\cdot x + 16) + \frac{1}{3} - 48[/tex]

By comparing each expression, the results are presented below:

[tex]r = 16[/tex], [tex]s = -48[/tex]

Answer:

75-52.5 =x

Step-by-step explanation:

We know that the total amount they eat is 75

They eat 52.5 is acacia leaves.  The rest is other types of leaves

75 - 52.5 = other types of leaves

75-52.5 =x

Answer:

See attachement

Step-by-step explanation:

The interval 0-20 on vertical axis will be skipped on paper graph and graph will start from 20.

Answer:

$5,368,709.12

Step-by-step explanation:

Kono Dio Da!!

Answer:

5368709.12

Step-by-step explanation:

i just did this earlier

Answer:

-0.86602540378 or -√3/2

Answer:

2.25 pounds

Step-by-step explanation:

The diagram showing the weight of bags with grapes is shown in the attached file below.

From the diagram; number of  bags of grapes that had a weight of [tex]\dfrac{3}{8}[/tex] pounds or less is:

[tex]\dfrac{3}{8}[/tex] pounds  = 3

[tex]\dfrac{1}{4}[/tex] pounds = 4

[tex]\dfrac{1}{8}[/tex] pounds = 1

Thus; the total is = 3+4+1 = 8

However, The total weight of the grapes in the bag that had a weight of  [tex]\dfrac{3}{8}[/tex] pounds or less is :

= [tex]\dfrac{3}{8}(3) + \dfrac{1}{4}(4) + \dfrac{1}{8}(1)[/tex]

= [tex]\dfrac{9}{8} + 1 + \dfrac{1}{8}[/tex]

= [tex]\dfrac{9+8+1}{8}[/tex]

= [tex]\dfrac{18}{8}[/tex]

= 2.25 pounds

Answer:

$58.415

Step-by-step explanation:

Initial value: 50 dollars

Independent variable: 5.3%

Dependent variable: Y

This equation can be written in slope intercept form:

[tex]y=mx+b[/tex]

[tex]y= 1.53x+50[/tex]

x= the number of years

[tex]y= 1.53(5.5)+50[/tex]

[tex]y=8.415+ 50[/tex]

[tex]y= 58.415[/tex]

Answer:

-9 and 2

Step-by-step explanation:

4 is the answer

The next best is 3

Answer:

0.5584 probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws.

Step-by-step explanation:

For each free throw, there are only two possible outcomes. Either she makes it, or she does not. The probability of making a free throw is independent of other free throws. So we use the binomial probability distribution to solve this question.

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.

The probability that Shruti succeeds at any given free-throw is 80%, percent.

This means that [tex]p = 0.8[/tex]

Sample of 12 free throws:

This means that [tex]n = 12[/tex]

Use her results to estimate the probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws.

[tex]P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12)[/tex]

In which

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

[tex]P(X = 10) = C_{12,10}.(0.8)^{10}.(0.2)^{2} = 0.2835[/tex]

[tex]P(X = 11) = C_{12,11}.(0.8)^{11}.(0.2)^{1} = 0.2062[/tex]

[tex]P(X = 12) = C_{12,12}.(0.8)^{12}.(0.2)^{0} = 0.0687[/tex]

[tex]P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12) = 0.2835 + 0.2062 + 0.0687 = 0.5584[/tex]

0.5584 probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws.

Answer:0.8

Step-by-step explanation:in 5 of the 25 stimulated trials, scrutiny continued federal than 10 successes

Answer:

S=288ft^2

Step-by-step explanation:

d=11.2ft, h=9.2ft

r=d/2=11.2/2=5.6

e=√r^2+h^2=√5.6^2+9.2^2

e=10.77ft

s=πr^2+πre

s=π(5.6)^2+π(5.6) (10.77)

s=91.67π

s≈288ft^2

If the slant height of the cone is 10.77 feet and the radius of the base circle is 5.6 feet. Then the surface area of the cone is 189.48 square feet.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The height of the cone is 9.2 feet and the diameter is 11.2 feet. Then the radius will be

r = d/2

r = 11.2/2

r = 5.6

Then the slant height of the cone will be

[tex]l = \sqrt{5.6^2 + 9.2}\\\\l = 10.77 \ \rm ft[/tex]

Then the surface area of the cone will be

[tex]\rm Surface \ area = \pi rl\\\\Surface \ area = \pi \times 5.6 \times 10.77\\\\Surface \ area = 189.48 \ ft^2[/tex]

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Answer:

1/80

Step-by-step explanation:

The probability of selecting each of the event in the sample space is; 1/80

We are given;

Sample Space = 80 separate events

Now, we are told that each event is equally likely to be selected.

Thus;

Probability of selecting each event = 1/80

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Answer:

2 1/4

Step-by-step explanation:

2 2/8

The top and bottom of the fraction can be divided by 2

2 1/4

Answer:

Cylinder

Step-by-step explanation:

The given geometric shape is of a cylinder.

Answer:

Cylinder

Step-by-step explanation:

The shape will make a cylinder if put together.

Answer:

median = 58

mean= 48.4

Step-by-step explanation:

to find the mean you add all of the numbers and divide it by 5 in this case

Answer:

x=4

Step-by-step explanation

Answer:

x = 4

Explanation:                                                                                                                  

Answer:

a = 2

Step-by-step explanation:

Note that a point uses (x , y).

y = 1

x = a

Plug in 1 for y in the equation, and a for x:

y = 3x - 5

1 = 3a - 5

Isolate the variable, a. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First add 5 to both sides:

1 (+5) = 3a - 5 (+5)

1 + 5 = 3a

6 = 3a

Next, divide 3 from both sides:

(6)/3 = (3a)/3

a = 6/3

a = 2

2 is your value for a.

~

Answer:

K, (-3.5,-5), E, (3.5, 3)

Step-by-step explanation:

Answer:

y= - 3/2x + 1