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3 years ago

HELP ASAP! 20 POINTS! 5 QUESTIONS!

Mathematics

1 answer:

Ainat [17]3 years ago

6 0

Answer:

1. Let the unknown number be x

The phrase “8 and” means addition so that’s 8 +

5 times a number is multiplication so that’s 5 times x, or simply, 5x

So the correct equation would be 8 + 5x = 43

And the correct value for variable x is 7

8 + 35 = 43

2. A

3. Here we can see that there has to be a single unknown variable and using that variable we have to create an equation. That equation will ultimately help us to find the exact value of the variable. This way we can easily reach the answer that is asked in the question.

Let us assume the length of the first piece = x

Length of the second piece = 2x

Length of the third piece = 6x

Now we can get to the equation

x + 2x + 6x = 180

9x = 180

x = 180/9

= 20

So the length of the first piece of the board is 20 feet.I hope i have explained the problem to your satisfaction and understanding

4. C

5. B

Step-by-step explanation:

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A baby elephant weighs 1,400 pounds, which is 7,437 pounds less than her mother. Write an equation to express the weight of the

erica [24]

Let's say that y is the weight of the mother and x is the weight of the baby.
We know that the baby is 7437 pounds less than the mother, which means you need to add 7437 pounds to the baby's weight to get the mother's.
We can show it like this:
x+7437=y.
We know what the baby's weight is (1400 lbs), so just sub it in:
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3 years ago

Three ice cream cones cost 8.25,at this rate how much does 2 ice creams cones cost for two cones

Sav [38]

Answer:

5.50

Step-by-step explanation:

If three cones cost 8.25, then each cone should cost 2.75. (8.25 / 3 = 2.75)

Then 2 cones should cost 5.50 (2.75 x 2 = 5.50)

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3 years ago

Ron is 8 years old and 40 inches tall. If he grows at the same rate every year, how tall was he when he was 5 years old?

Vadim26 [7]

He would be 25 inches tall.

40 divided by 8 would equal 5 so at age 1, he was 5 inches tall. So 5 times 5 which is how old he was, would equal 25 inches.

5 0

2 years ago

Read 2 more answers

In October of 2012, Apple introduced a much smaller variant of the Apple iPad, known at the iPad Mini. Weighing less than 11 oun

sveticcg [70]

Answer:

a. $f_X(x) = \dfrac{1}{3.5}8.5$

b. the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c. the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e. 86 should have a battery life of at least 9 hours

Step-by-step explanation:

From the given information;

Let X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability density function can now be determined as :

$f_X(x) = \dfrac{1}{B-A}A$

where A and B are the two parameters of the uniform distribution

From the question;

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours

So; Let A = 8,5 and B = 12

Therefore; the mathematical expression for the probability density function of battery life is :

$f_X(x) = \dfrac{1}{12-8.5}8.5$

$f_X(x) = \dfrac{1}{3.5}8.5$

b. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

The probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:

F(x) = P(X ≤x)

$F(x) = \dfrac{x-A}{B-A}$

$F(10) = \dfrac{10-8.5}{12-8.5}$

F(10) = 0.4286

the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?

The battery life for an iPad Mini will be at least 11 hours is calculated as follows:

$P(X\geq11) = \int\limits^{12}_{11} {\dfrac{1}{3.5}} \, dx$

$P(X\geq11) = {\dfrac{1}{3.5}} (x)^{12}_{11}$

$P(X\geq11) = {\dfrac{1}{3.5}} (12-11)$

$P(X\geq11) = {\dfrac{1}{3.5}} (1)$

$P(X\geq11) = 0.2857$

the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?

$P(9.5 \leq X\leq11.5) =\int\limits^{11.5}_{9.5} {\dfrac{1}{3.5}} \, dx$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} \, (x)^{11.5}_{9.5}$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (11.5-9.5)$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (2)$

$P(9.5 \leq X\leq11.5) =0.2857* (2)$

$P(9.5 \leq X\leq11.5) =0.5714$

Hence; the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?

The probability that battery life of at least 9 hours is calculated as:

$P(X \geq 9) = \int\limits^{12}_{9} {\dfrac{1}{3.5}} \, dx$

$P(X \geq 9) = {\dfrac{1}{3.5}}(x)^{12}_{9}$

$P(X \geq 9) = {\dfrac{1}{3.5}}(12-9)$

$P(X \geq 9) = {\dfrac{1}{3.5}}(3)$

$P(X \geq 9) = 0.2857*}(3)$

$P(X \geq 9) = 0.8571$

NOW; The Number of iPad that should have a battery life of at least 9 hours is calculated as:

n = 100(0.8571)

n = 85.71

n ≅ 86

Thus , 86 should have a battery life of at least 9 hours

3 0

3 years ago

What is one of the solutions to the following system of equations?

Amanda [17]

Answer:

(8,-1)

Step-by-step explanation:

Given : $x^{2} +y^{2} =65$

$x+y=7$

To Find: solution of given system of equations.

Solution:

Equation a : $x^{2} +y^{2} =65$

Equation b : $x+y=7$

Substitute the value of y from equation b in equation a

y from equation b : y = 7-x

Now substitute value of y in equation a

Thus equation a becomes:

$x^{2} +(7-x)^{2} =65$

$x^{2} +49+x^{2}-14x =65$

$2x^{2} -14x =65-49$

$x^{2} -7x -8=0$

$x^{2} -8x+x -8=0$

$x(x-8)+1(x-8)=0$

$(x+1)(x-8)=0$

⇒ x= -1 and x = 8

Now substitute values of x in equation b to obtains values of y

⇒ $x+y=7$

for x = -1

⇒ $-1+y=7$

⇒ $y=7+1$

⇒ $y=8$

Thus (x,y)=(-1,8)

For x =8

⇒ $8+y=7$

⇒ $y=7-8$

⇒ $y=-1$

Thus (x,y)=(8,-1)

Hence Option A is the correct solution .

6 0

3 years ago

Read 2 more answers