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max2010maxim [7]
3 years ago
5

Jake is using a horse trailer to take his horses to his new ranch. 1 Horse= 1,200 lb Trailer= 2,700 lb Jake's truck can tow a ma

ximum weight of 5,000 pounds. What is the maximum number of horses he can take in his trailer at one time without going over the maximum weight his truck can tow?
Mathematics
1 answer:
Kitty [74]3 years ago
3 0

Answer:

Jack can take only 1 horse on his trailer to be towed by the truck without going over the maximum weight the truck.

Step-by-step explanation:

Given:

Weight of 1 horse = 1,200 lb

Weight of trailer = 2,700 lb

Jacks'truck can tow a maximum of 5000 pounds.

To find the maximum number of horses Jack can take in his trailer without going over the maximum weight his truck can tow.

Solution:

Let the maximum number of horses that Jack can take be = x

Using unitary method to find weight of x horses.

If 1 horse weights = 1,200 lb

Then x horses will weight in lbs = 1,200\times x = 1,200x

Total weight of horses and trailer in lbs = 1200x+2700

Since the maximum weight the truck can tow = 5,000 lb, so the inequality can be given as:

1200x+2700\leq5000

Subtracting both sides by 2700.

1200x+2700-2700\leq5000-2700

1200x\leq2300

Dividing both sides by 1200.

\frac{1200x}{1200}\leq\frac{2300}{1200}

x\leq1.91

From the inequality solution for x, we can conclude that Jack can take only 1 horse on his trailer to be towed by the truck without going over the maximum weight the truck.

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Find the measure of each acute angle.<br><br> (3x + 2)∘ = and x∘ =
rusak2 [61]

Answer:

The measure of one of the acute angles is 22 degrees, and the measure of the other acute angle is 68 degrees.

Step-by-step explanation:

The angles of a triangle add up to 180 degrees; we know this by the Sum of Angles of a Triangle Theorem.

Then one angle is marked as a right angle meaning it has a measure of 90 degrees.

Using this information and the labels on the diagram we can set up an equation:

x+3x+2+90=180

Now we can solve for x.

4x+92=180

4x=88

x=22 degrees

The measure of one of the acute angles is 22 degrees.

Now to solve for the measure of the other acute angle.

Subsitute the value of x first.

x=22

(3x+2)=?

3*22+2=68 degrees

The measure of the other acute angle is 68 degrees.

4 0
2 years ago
Read 2 more answers
A bank branch located in a commercial district of a city has the business objective of improving the process for serving custome
choli [55]

Answer:

We conclude that the mean waiting time is more than or equal to 5 minutes at 5% level of significance.

Step-by-step explanation:

We are given that waiting time is defined as the time the customer enters the line until he or she reaches the teller window.  

A random sample of 15 customers is selected. Results found that the sample mean waiting time was 4.287 minutes with a sample standard deviation of 1.638 minutes.

Let \mu = <u><em>mean waiting time.</em></u>

SO, Null Hypothesis, H_0 : \mu \geq 5 minutes     {means that the mean waiting time is more than or equal to 5 minutes}

Alternate Hypothesis, H_A : \mu < 5 minutes      {means that the mean waiting time is less than 5 minutes}

The test statistics that would be used here <u>One-sample t-test statistics</u> as we don't know about population standard deviation;

                              T.S. =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean waiting time = 4.287 minutes

            s = sample standard deviation = 1.638 minutes

            n = sample of customers = 15

So, <u><em>the test statistics</em></u>  =  \frac{4.287 -5}{\frac{1.638}{\sqrt{15} } }  ~ t_1_4

                                       =  -1.686

The value of t test statistics is -1.686.

Since, in the question we are not given the level of significance so we assume it to be 5%. <u>Now, at 5% significance level the t table gives critical value of -1.761 at 14 degree of freedom for left-tailed test.</u>

Since our test statistic is more than the critical value of t as -1.686 > -1.761, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u><em>we fail to reject our null hypothesis</em></u>.

Therefore, we conclude that the mean waiting time is more than or equal to 5 minutes.

5 0
3 years ago
Date:
Vilka [71]
$83.60 in gross wages
4 0
2 years ago
Find area of blue shaded region
RUDIKE [14]

Answer:

\approx \: 7.33 \:  {cm}^{2}

Step-by-step explanation:

Area of the blue shaded region

=  \frac{ \theta}{360 \degree}  \times \pi r_1^2  - \frac{ \theta}{360 \degree}  \times \pi r_2^2  \\  \\  =   \frac{ \pi\theta}{360 \degree} ( r_1^2 - r_2^2) \\  \\ ( r_1 = 4 \: cm, \:  \:  r_2 = 3\: cm, \:  \:  \theta = 120 \degree) \\  \\ =   \frac{ 3.14 \times 120 \degree}{360 \degree} ( 4^2 - 3^2) \\  \\  =   \frac{ 3.14 }{3}  \times 7 \\  \\  =  \frac{21.98}{3}  \\  \\  = 7.32666667 \\  \\  \approx \: 7.33 \:  {cm}^{2}

8 0
3 years ago
If the area is 27 meters &amp; 6 meters is the height what is the length ?
bezimeni [28]
Area= legnth times width
or sometimes
area=legnth times height
area=measure1 times measure 2 on a flat plane
dependson the names

area=27
height=6
area=legnth times height
subsitute
27=legnth times 6
divide both sides by 6
27/6= legnth
simplified to 4 and 3/4
legnth=4 and 3/4 meter
subsitute
8 0
3 years ago
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