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2 years ago

a teacher had 21 red pens. if the ratio of red pens to blue pens she owned was 3:1 , how many pens did she have in total

Mathematics

2 answers:

snow_lady [41]2 years ago

8 0

She had 21:7 because if you multiply 3:1 by 7 each it is 21:7 so she had 7 blue pens

erma4kov [3.2K]2 years ago

5 0

There are 21 red pens. For every 3 red pens, there is 1 blue pen.
Let's make these into a fraction equation.
21/p=3/1
p is the number of blue pens we have yet to find.
First, cross multiply.
21x1=21
px3=3p
Now, we have an equation of
21÷3p
We set it equal to 1, and we solve it.
21÷3p = 1
(21÷3p)×3p=1×3p
21=3p
21÷3=(3p)÷3
7=p
So, if there are 21 red pens, there are 7 blue pens.
We add these together to find the total number of pens the teacher has.
21+7=28
The teacher has 28 pens total.

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Several years ago, 39% of parents who had children in grades K-12 were satisfied with the quality of education the students r

BaLLatris [955]

<h2>Answer with explanation:</h2>

Let p be the population proportion of parents who had children in grades K-12 were satisfied with the quality of education the students receive.

Given : Several years ago, 39% of parents who had children in grades K-12 were satisfied with the quality of education the students receive.

Set hypothesis to test :

$H_0: p=0.39\\\\H_a :p\neq0.39$

Sample size : n= 1055

Sample proportion : $\hat{p}=\dfrac{466}{1055}=0.441706161137\approx0.44$

Critical value for 95% confidence : $z_{\alpha/2}=1.96$

Confidence interval : $\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}$

$0.44\pm (1.96)\sqrt{\dfrac{0.39(1-0.39)}{1055}}\\\\0.44\pm0.0299536805135\\\\0.44\pm0.03\\\\=(0.44-0.03, 0.44+0.03)\\\\=(0.41,\ 0.47)$

Since , Confidence interval does not contain 0.39.

It means we reject the null hypothesis.

We conclude that 95% confidence interval represents evidence that parents' attitudes toward the quality of education have changed.

8 0

3 years ago

How to use inverse cosin

Alecsey [184]

Answer:

sec

Step-by-step explanation:

1/cosin = sec or cosin^-1

4 0

2 years ago

If 15 is added to a number the result is 56 less than twice the number

mart [117]

Let, the number = x
It would be: x + 15 = 2x - 56
2x - x = 15 + 56
x = 71

In short, Your Answer would be 71

Hope this helps!

3 0

3 years ago

1.) You are one of five people who have been hired to mow the lawn at the local college. Each week, the dimensions of the plot y

iren [92.7K]

Answer:

1a) Length = 7x + 3 & Width = 4x - 2

1b) Area = $28x^2 -2x -6$

1c) Area = 2774 sq. m

2. $(x-4)(y+7)$

Step-by-step explanation:

1a)

The length given as words is "3 more than 7 times x"

The width given as words is "4 times x minus 2"

The expression for length would be 7x + 3

The expression for width would be 4x - 2

1b)

The area is length * width

Since we already know the algebraic expressions for length and width from part (a) above, we use the formula:

Area = (7x+3)(4x-2) = 28x^2 -14x + 12x - 6 = 28x^2 -2x -6

Area = $28x^2 -2x -6$

1c)

Given x = 10, we put this into the area expression we found in (b) above.Let's see:

$28x^2 -2x -6\\=28(10)^2 -2(10) -6\\=2774$

Area = 2774 sq. m

We can group the first two terms and next two terms and write up:

$xy-4y+7x-28\\(xy-4y)+(7x-28)\\y(x-4)+7(x-4)\\(x-4)(y+7)$

That's the factored form.

8 0

3 years ago

Read 2 more answers

An object moves in simple harmonic motion with period 8 seconds and amplitude 6 cm. At time t = 0 seconds, its displacement d fr

Vladimir79 [104]

In the equation model, the simple harmonic motion is d=6sin(πt/4)-6 if the object moves in simple harmonic motion with a period of 8 seconds and amplitude of 6 cm.

<h3>What is simple harmonic motion?</h3>

Simple Harmonic Motion is described as a motion in which the restoring force is proportionate to the body's displacement from its mean position.

We have:

Amplitude A = 6 cm

Time period = 8 seconds

T = 2π/w

8 = 2π/w

w = π/4

Its displacement d from rest is -6 cm, and initially, it moves in a positive direction.

d(0) = -6 cm at t = 0

The equation becomes:

$\rm d = 6sin(\dfrac{\pi}{4}t)-6$

Thus, in the equation model, the simple harmonic motion is d=6sin(πt/4)-6 if the object moves in simple harmonic motion with a period of 8 seconds and amplitude of 6 cm.

Learn more about the simple harmonic motion here:

brainly.com/question/17315536

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4 0

2 years ago