Part 1Simplifyeach fraction. Some fractions can be simplified more than once A 110/390

Answer:

Step-by-step explanation:

first from the lower triangle, the unknown length is [tex]\sqrt{10^2-4^2} =\sqrt{100-16}=\sqrt{84}[/tex] so then x is equal to [tex]\sqrt{84-4^2}=\sqrt{68}[/tex] or about 8.2

The number of gorillas at the safari park is 4.

Let the number of gorillas at the safari park be x.

It is given that there are 24 more buffalo than there are gorillas.

Number of buffalo at the safari park = 24 + x

There are 7 times as many wallabies as there are gorillas.

Number of wallabies at the safari park = 7x

Now, the number of buffalo is the same as the number of wallabies.

So, we equate their numbers to find the value of x i.e. number of gorillas.

24 + x = 7x

7x - x = 24

6x = 24

x = 4

Therefore, the number of gorillas at the safari park is 4.

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Answer:

9/20

Step-by-step explanation:

3/10 + 1/4

find a common denominator, which is 20 here

6/20 + 5/20 = 11/20 he used

left over is 9/20

Answer:

y = (5/2)x - 4

Step-by-step explanation:

(0, -4) and (2, 1)

(x₁, y₁)         (x₂, y₂)

        y₂ - y₁         1 - (-4)         1 + 4        5

m = ------------- = ------------ = --------- = --------

         x₂ - x₁         2 - 0            2            2

y - y₁ = m(x - x₁)

y - (-4) = (5/2)(x - 0)

y + 4 = (5/2)x - 0

   -4                 -4

----------------------------

y = (5/2)x - 4

I hope this helps!

The price of the house will double the original value in 35 years

The given parameters from the question are

Initial value of the house = $265,100

Rate of gain = 2% of its value every year

An exponential function is represented as

y = a *(1 + r)^x

Where

This means that

a = 265,100

r = 2%

So, we have

y = 265,100 *(1 +2%)^t

When the price doubles, we have

2 * 265,100 = 265,100 *(1 +2%)^t

Divide both sides by 265,100

So, we have

2  = (1 +2%)^t

Evaluate the sum

So, we have

2 = 1.02^t

Take the logarithm of both sides

t * log(1.02) = log(2)

Divide

t = log(2)/log(1.02)

Evaluate

t = 35

Hence, the number of years is 35

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ieven

raph of the fucnction

ind

quation of the fuctcion

xpolanation

s we see it i s the graph of exponential function.

from graph we find point (0 , 2)

now , we substitute this point to find the equation.

so , this exponential function satisfy the point.

Final Answer

ence , the correct option is 1,.

Answer:

i cannot see the lines very well, but i can tell you how to find slope

Step-by-step explanation:

slope is rise/run. find where the line hits a intersection on the graph, and count the squares across the graph where it hits another intersection. it should not be on the line though, because that is only the run. then count how many squares up it takes till you touch where the line hits another intersection. that is the rise. then divide the rise by the run.

Answer:

[tex]5 \times 10^4[/tex]

Step-by-step explanation:

Let the number of grains of rice be g.

[tex]\frac{g}{1}=\frac{1}{2 \times 10^{-5}} \\ \\ g=\frac{1}{2} \times 10^5 \\ \\ =5 \times 10^4[/tex]

Step-by-step explanation:

0.75x+2

2 is taken and 0.75 is not optional therfore

0.75=x(per square foot) =0.75x

and

$2 fee is required

so they must pay 2 dollars plus 0.75 everysquare foot

answer:

0.75x+2

The interest that they will they have to pay if it takes them 4 years and 3 months to repay the loan is $1377.

From the information, Isaac's parents borrow $3600.00 from the bank for new appliances for their kitchen and the simple interest rate is 9% per year.

Principal = $3600

Rate = 9%

Time = 4 years 3 months = 4.25

It should be noted that simple interest is calculated as:

= Principal × Rate × Time / 100

= (3600 × 9 × 4.25) / 100

= 137700 / 100

= $1377

Therefore, the interest is $1377.

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The distance travelled by Jack to Mexico on Tuesday is 876 miles.

The distance travelled by Jack to Mexico on Wednesday is 986 miles.

To determine the total miles he drove ,

The sum of the distance travelled by Jack to Mexico on Tuesday and Wednesday.

Let the total miles drove is denoted as T.

Thus the total miles drove is 1862 miles.

Answer:

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Given the set of data:

12, 4, 11, 3, 4, 0, 13, 13, 2, 6, 11, 0, 10, 11, 3, 4, 0, 10, 13, 2, 11, 9.

Let's complete the given frequency table using the set of data given.

Frequency can be said to be the number of times a number occurs in a set of data.

hus, we have:

• 0 - 2

ubmbers between 0 - 2 in the data set: 0, 2, 0, 0, 2 ==> 5 times

• 3 - 5

3 - 5: 4, 3, 4, 3, 4, ==> 5 times

• 6 - 8:

6 - 8: 6, ==> 1 time

• 9 - 11:

: 9 - 119, 11, 11, 10, 11, 10, 11, 9 ==> 7 times

• 12 - 14:

12 - 134: 12, 13, 13, 13 =3 ==> 4 times.

Therefore, the complete table is:

The Slope-Intercept Form of the equation of a line is:

Where "m" is the slope of the line and "b" is the y-intercept.

You have the first line:

You can identify that the y-intercept is:

You can find the x-intercept substituting the following value of "y" into the equation of the line:

And, after the substitution, you can solve for "x":

Now you know that the first line passes through these points:

Then, you can graph it.

Given the second line:

You can identify that:

And you can find the x-intercept by following the same procedure applied for the first line:

Then, this line passes through these points:

Now you can graph it.

See the graph below:

By definition, when the lines intersect, the solution of the System of equations is the point where the two lines intersect.

The answer is: First option.

Answer: μ=​20, σ=4.0

Step-by-step explanation:

Answer:

omg what is standard deviation that was on my psat today

Given ratio:

Multiply both sides by the L.C.M of their denominator

The L.C.M of 2 and 4 is 4

Hence:

The true statements about the solutions to this number line include the following:

A. -1 is a solution.

E. -1.5 is a solution.

F. All negative numbers are solutions.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.

This ultimately implies that, a number line can be used to determine the difference between two numbers such as 23 and 12. Also, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.

In conclusion, we can reasonably infer and logically deduce that an inequality which represent the solutions to this number line in interval notation is given by: -1 ≤ x ≤ ∞.

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Answer:

z = 6

Step-by-step explanation:

The angle in the middle is a right angle with a measure of 90°

Together, all three angles, makes a stright angle which is measured 180°.

So we can write the following equation to find the value of z:

5z + 1 + 59 = 90 (we don'thave to include the middle angle since we already its measure)

add like terms

5z + 60 = 90 subtract 60 from both sides

5z = 30 divide both sides by 5

z = 6

The track lap time of the runner will be 3 3/5 minutes.

From the information, the runner has a track lap time of 1 minute while at a run, 4 minutes while at a jog, and 7 minutes while at a walk. If 2/5 of the lap is paced at a run, 1/3 at a jog, and 4/15 at a walk.

The track lap time of the runner will be:

= (2/5 × 1 minute) + (1/3 × 4 minutes) + (4/15 × 7 minutes)

Note that 1 minute = 60 seconds

(2/5 × 1 minute) + (1/3 × 4 minutes) + (4/15 × 7 minutes)

= 24 seconds + 80 seconds + 112 seconds

= 216 seconds

= 3 minutes 36 seconds.

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[tex]\frac{2.4}{10^{4} }[/tex] is the simplest form of scientific notation.

In mathematical notation, operations, unnamed numbers, relations, and any other mathematical objects are represented by symbols that are combined into expressions and formulae. Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be expressed as 6.5 108 in scientific notation. A system of symbols for designating unique items. Example: In mathematics, the symbol "∞" stands for "infinity." There are many notations in mathematics.

Given Data

8.1×10^−7

3×10^−3

Dividing

[tex]\frac{8.1(10}{3(10}[/tex]⁷₃

[tex]\frac{8.1}{3}[/tex] × 10⁻⁷⁻⁽⁻³⁾

2.7 × 10⁻⁴

[tex]\frac{2.4}{10^{4} }[/tex]

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Answer:

Equation

Step-by-step explanation:

Equations require equal signs.

Answer:

it is 1,152

Step-by-step explanation:

4×3=12×96=1,152

Answer:a

Step-by-step explanation:

Answer:

(a) There are 22 workers are available in the factory.

Step-by-step explanation:

(a) Let the number of workers in the factory be x.

Basic rate = $15

Working hours in a week  = 48 hours

Total wages in a week = $ 15840

If no overtime is to be paid then according to question,

Amount paid to 1 worker = 48 X 15 = $ 720

Amount paid to x worker = 720x

15840 = 720

x = 15840/720

x = 22

Answer:

you know it's a very good question

Step-by-step explanation:

I have no idea

The area under the standard normal curve between z=0 and z=3 is 0.4987.

It should be noted that because the normal distribution is symmetrical on both sides of the mean and is a continuous probability distribution, the right side of the center is the opposite of the left side.

The normal distribution was first termed by early statisticians who observed that the same shape repeatedly appeared in many distributions. The characteristics of normal distributions are as follows: Bell-like in its symmetry. The distribution's mean and median, which are both at its center, are equal.

The area will be illustrated as:

P(0 < Z < 3)

From the distribution table. In this case, it's important to look at the normal distribution table under the z score for the values of zero less than Z and Z less than 3. This will be:

= 0.9987 - 0.5

= 0.4987

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The statement that is not true is that at this rate, it would take less than 10 mins for the temperature of the liquid to rise to 52 degrees.

We know that in a graph we see the presentation of a data set by the use of the Cartesian coordinates. There is the vertical axis and there is the horizontal axis. The vertical axis is the axis where we have to plot the time while the vertical axis is the axis where we have to plot the temperature as we can see from the image attached to this answer.

The graph as show has to the points which are; (0, 0) and (6.5, 26). Thus we can use the both points to obtain the slope of the graph and this would give us;

m = 26 - 0/ 6.5 - 0

m = 4

This implies that the rate at which the temperature rise with time is 4 degrees centigrade per hour. In a quarter hour, the temperature would rise to;

y = mx

y = 4(15)

y = 60 degrees centigrade.

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ANSWER

t = 10.27

EXPLANATION

Step 1: Given

Step 2: Divide both sides by 500

Step 3: Take the natural logarithm of both sides

Step 4: Divide both sides by 0.0675

Hence, t = 10.27 (rounded to the nearest hundredth).