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mr Goodwill [35]

2 years ago

13

Mick paid $2.94 in sales tax on an item that cost $42.00 before tax. At that rate, how much would he paying sales tax before an

item that cost $58 before tax

1 answer:

sergiy2304 [10]2 years ago

5 0

To answer this question you would have two steps involved. The first step would be to find the percentage of $42 that gives us $2.94. Set up an equation 42x=2.94. Divide both sides by 42 to get the decimal 0.07. This equal 7%. Take this percentage multiplied by the $58. You need to change the 7% into 0.07 to be able to calculate it. 0.07 x 58 = $4.06 sales tax.

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Which statement is an example of the symmetric property of congruence?

olchik [2.2K]

The symmetric property of congruence states that if a quantity, say, A is congruent to a quantity, say B, then, the quantity B is congruent to the quantity A.

Mathematically, this statement of the symmetric property of congruence can be written as:

If $A\cong B$ , then $B\cong A$ .

Applying this symmetric property of congruence to the question that we are given, we see that only Option D fulfills the conditions of the definition of the property of congruence as Option D clearly states that:

If $\Delta EFG\cong \Delta HJK$ , then $\Delta HJK\cong \Delta EFG$ which is the exact statement of the symmetric property of congruence when applied to triangles.

Thus, Option D is the correct option.

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1 year ago

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I NEED HELP PLEASE! Jenny's birthday cake is circular and has a 30 cm radius. Her slice creates an arc of with a central angle o

dybincka [34]

Ok, so if the angle is 120 degrees, its one third of the full cake (which is 360 degrees). So the area of the whole circle (worked out with area = pi * r^2 where r is 30) gives 900*pi, and so one third of that (because her slice is one third) is 300pi.

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2 years ago

A gallon of Moo Milk costs \$5.12$5.12dollar sign, 5, point, 12. What is the price, in dollars, of an 888 ounce glass of Moo Mil

Sladkaya [172]

The correct statement is:
A gallon of Moo Milk costs $5.12 What is the price, in dollars, of an 8 ounce glass of Moo Milk? There are 128 ounces in 1 gallon.

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1 gallon = 128 ounces, so we can write:

Cost of 128 ounces of Moo Milk = $ 5.12

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Thus, 8 ounces of Moo Milk will cost $ 0.32

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2 years ago

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Ben and Josh went to the roof of their 40-foot tall high school to throw their math books offthe edge.The initial velocity of Be

Taya2010 [7]

Answer

Josh's textbook reached the ground first

Josh's textbook reached the ground first by a difference of $t=0.6482$

Step-by-step explanation:

Before we proceed let us re write correctly the height equation which in correct form reads:

$h(t)=-16t^2 +v_{o}t+s$ Eqn(1).

Where:

$h(t)$ : is the height range as a function of time

$v_{o}$ : is the initial velocity

$s$ : is the initial heightin feet and is given as 40 feet, thus Eqn(1). becomes:

$h(t)=-16t^2 + v_{o}t + 40$ Eqn(2).

Now let us use the given information and set up our equations for Ben and Josh.

<u>Ben:</u>

We know that $v_{o}=60ft/s$

Thus Eqn. (2) becomes:

$h(t)=-16t^2+60t+40$ Eqn.(3)

<u>Josh:</u>

We know that $v_{o}=48ft/s$

Thus Eqn. (2) becomes:

$h(t)=-16t^2+48t+40$ Eqn. (4).

<em><u>Now since we want to find whose textbook reaches the ground first and by how many seconds we need to solve each equation (i.e. Eqns. (3) and (4)) at </u></em> $h(t)=0$ <em><u>. Now since both are quadratic equations we will solve one showing the full method which can be repeated for the other one. </u></em>

Thus we have for Ben, Eqn. (3) gives:

$h(t)=0-16t^2+60t+40=0$

Using the quadratic expression to find the roots of the quadratic we have:

$t_{1,2}=\frac{-b+/-\sqrt{b^2-4ac} }{2a} \\t_{1,2}=\frac{-60+/-\sqrt{60^2-4(-16)(40)} }{2(-16)} \\t_{1,2}=\frac{-60+/-\sqrt{6160} }{-32} \\t_{1,2}=\frac{15+/-\sqrt{385} }{8}\\\\t_{1}=4.3276 sec\\t_{2}=-0.5776 sec$

Since time can only be positive we reject the $t_{2}$ solution and we keep that Ben's book took $t=4.3276$ seconds to reach the ground.

Similarly solving for Josh we obtain

$t_{1}=3.6794sec\\t_{2}=-0.6794sec$

Thus again we reject the negative and keep the positive solution, so Josh's book took $t=3.6794$ seconds to reach the ground.

Then we can find the difference between Ben and Josh times as

$t_{Ben}-t_{Josh}= 4.3276 - 3.6794 = 0.6482$

So to answer the original question:

<em>Whose textbook reaches the ground first and by how many seconds?</em>

Josh's textbook reached the ground first
Josh's textbook reached the ground first by a difference of $t=0.6482$

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1 year ago

Crop researchers plant 15 plots with a new variety of corn. The yields in bushels per acre are: 138.0 139.1 113.0 132.5 140.7 10

son4ous [18]

There is a relationship between confidence interval and standard deviation:
$\theta=\overline{x} \pm \frac{z\sigma}{\sqrt{n}}$
Where $\overline{x}$ is the mean, $\sigma$ is standard deviation, and n is number of data points.
Every confidence interval has associated z value. This can be found online.
We need to find the standard deviation first:
$\sigma=\sqrt{\frac{\sum(x-\overline{x})^2}{n}$
When we do all the calculations we find that:
$\overline{x}=123.8\\ \sigma=11.84$
Now we can find confidence intervals:
$($90\%,z=1.645): \theta=123.8 \pm \frac{1.645\cdot 11.84}{\sqrt{15}}=123.8 \pm5.0\\($95\%,z=1.960): \theta=123.8 \pm \frac{1.960\cdot 11.84}{\sqrt{15}}=123.8 \pm 5.99\\ ($99\%,z=2.576): \theta=123.8 \pm \frac{2.576\cdot 11.84}{\sqrt{15}}=123.8 \pm 7.87\\$
We can see that as confidence interval increases so does the error margin. Z values accociated with each confidence intreval also get bigger as confidence interval increases.
Here is the link to the spreadsheet with standard deviation calculation:
https://docs.google.com/spreadsheets/d/1pnsJIrM_lmQKAGRJvduiHzjg9mYvLgpsCqCoGYvR5Us/edit?usp=sharing

6 0

2 years ago