The ratio of sailboats to dinghies in the bay was 5 to 7 If there were 70

sailboats in the bay, how many dinghies were there?

Answers

Answer 1

Answer:

98

Step-by-step explanation:

Let the sailboats be s and the dinghies be d.

We have that:

s : d = 5 : 7

In other words:

s / d = 5 / 7

If there are 70 sailboats, this implies that s = 70

=> 70 / d = 5 / 7

=> d = (70 * 7) / 5 = 490 / 5 = 98

There will be 98 dinghies.


Related Questions

In July of 1997, Australians were asked if they thought unemployment would increase, and 47% thought that it would increase. In November of 1997, they were asked again. At that time 284 out of 631 said that they thought unemployment would increase ("Morgan gallup poll," 2013). At the 5% level, is there enough evidence to show that the proportion of Australians in November 1997 who believe unemployment would increase is less than the proportion who felt it would increase in July 1997?

Answers

Answer:

[tex]z=\frac{0.45 -0.47}{\sqrt{\frac{0.47(1-0.47)}{631}}}=-1.007[/tex]  

Now we can find the p value with the alternative hypothesis and using this probability:

[tex]p_v =P(z<-1.007)=0.157[/tex]  

Since the p value is higher than the significance level given of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion of interest is not significantly lower than 0.47

Step-by-step explanation:

Information given

n=631 represent the random sample selected

X=284 represent the people who said that they thought unemployment would increase

[tex]\hat p=\frac{284}{631}=0.45[/tex] estimated proportion of people who said that they thought unemployment would increase

[tex]p_o=0.47[/tex] is the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level

z would represent the statistic

[tex]p_v{/tex} represent the p value

System of hypothesis

We want to verify if the proportion of Australians in November 1997 who believe unemployment would increase is less than the proportion who felt it would increase in July 1997 (0.47), then the system of hypothesis are:  

Null hypothesis:[tex]p\geq 0.47[/tex]  

Alternative hypothesis:[tex]p < 0.47[/tex]  

The statistic would be given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]z=\frac{0.45 -0.47}{\sqrt{\frac{0.47(1-0.47)}{631}}}=-1.007[/tex]  

Now we can find the p value with the alternative hypothesis and using this probability:

[tex]p_v =P(z<-1.007)=0.157[/tex]  

Since the p value is higher than the significance level given of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion of interest is not significantly lower than 0.47

3. Jada is making a scale model of the solar system. The distance from Earth to the
moon is about 2.389 x 10 miles. The distance from Earth to the sun is about
9.296 X 10' miles. She decides to put Earth on one corner of her dresser and the
moon on another corner, about a foot away. Where should she put the sun?
o On a windowsill in the same room?
o In her kitchen, which is down the hallway?
o A city block away?
Explain your reasoning.

Answers

Answer:

kitchen

Step-by-step explanation:

if a foot is 2.389 then i would be pretty far but not a block away

The "Jupiter Bar" is a candy bar that is only manufactured and sold in one size. Tens of thousands of bars are manufactured every day. Nutritional content appears on the bar's wrapper, including a statement that a given bar has a sodium content of 96 milligrams.
Due to variability inherent in all manufacturing, we know that some bars would have slightly less than 96 milligrams of sodium and some bars would have more than 96 milligrams of sodium even if the value of "96 milligrams" appears on the wrapper. However, there is a concern that the average sodium content in all Jupiter Bars is actually more than 96 milligrams, and we have been asked to investigate.
Below are the sodium measurements (in milligrams) from a sample of 20 Jupiter Bars:
88 93 99 104
98 103 96 99
111 90 108 98
101 112 104 102
105 101 95 104
Summary statistics:
n = 20
sample mean = 100.55
sample standard deviation = 6.304
Q = 97: median = 101: Q3 = 104
a) Test whether the sample provides evidence at the 5% level of significance that the average sodium content in all Jupiter Bars is actually more than 96 milligrams.

Answers

Answer:

We conclude that the average sodium content in all Jupiter Bars is actually more than 96 milligrams.

Step-by-step explanation:

We are given that there is a concern that the average sodium content in all Jupiter Bars is actually more than 96 milligrams, and we have been asked to investigate.

Summary statistics:

n = 20

sample mean = 100.55

sample standard deviation = 6.304

Q = 97: median = 101: Q3 = 104

Let [tex]\mu[/tex] = average sodium content in all Jupiter Bars.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 96 milligrams     {means that the average sodium content in all Jupiter Bars is equal to 96 milligrams}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 96 milligrams     {means that the average sodium content in all Jupiter Bars is actually more than 96 milligrams}

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

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

where, [tex]\bar X[/tex] = sample mean sodium content = 100.55

            s = sample standard deviation = 6.304

            n = sample of Jupiter bars = 20

So, the test statistics  =  [tex]\frac{100.55-96}{\frac{6.304}{\sqrt{20} } }[/tex]  ~ [tex]t_1_9[/tex]

                                       =  3.228

The value of t test statistics is 3.228.

Now, at 5% significance level the t table gives critical value of 1.729 at 19 degree of freedom for right-tailed test.

Since our test statistic is more than the critical value of t as 3.228 > 1.729, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the average sodium content in all Jupiter Bars is actually more than 96 milligrams.

Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing! CHECK ALL THAT APPLY

Answers

Answer:

E 39

Step-by-step explanation:

x+6 = 45

Subtract 6 from each side

x+6-6 = 45-6

x = 39

Fie triunghiul ABC isoscel cu AB=AC=3 cm daca mediatoarea laturi AC intersectat cu latura BC in M si perimetrul thriunghiului AMC=12 cm.Calculati MC

Answers

Answer:

MC = 4.5cm

Step-by-step explanation:

Question:

Let the isosceles triangle ABC with AB = AC = 3 cm. if the mediator of the sides AC intersects with the side BC in M ​​and the perimeter of the triangle AMC = 12 cm. Calculate MC.

Solution:

Find attached the diagram used in solving the question.

Given:

∆ABC is an isosceles triangle (two sides and angles are equal)

AB = BC = 3cm

Perimeter of ∆AMC = 12cm

From the diagram, M cuts AC at the the middle.

AD = CD = AC/2 = 3/2

Perimeter of Right angled ∆AMD = AM + AD + MD

= 3/2 + AM +MD

Perimeter of Right angled ∆CMD =CM + CD + MD

= 3/2 + CM +MD

Right angled ∆AMD = Right angled ∆CMD

CM = AM

Therefore ∆AMC is an isosceles triangle

CM = AM (two sides of an isosceles triangle are equal)

Let CM = AM = x

Perimeter of ∆AMC = AM + CM + AC

12 = x + x + 3

12 = 2x + 3

2x = 12-3

2x = 9

x = 9/2 = 4.5

CM = AM = 4.5cm

MC = CM = 4.5cm

The base of a parallelogram measures 14 cm, and the height is unknown. The area of the parallelogram is more than 42 square cm. Which graph represents all possible values for the height of the parallelogram?
A number line going from negative 1 to positive 7. An open circle is at 3. Everything to the right of the circle is shaded.
A number line going from negative 1 to positive 7. An open circle is at 3. Everything to the left of the circle is shaded.
A number line going from 24 to 32. An open circle is at 28. Everything to the right of the circle is shaded.
A number line going from 24 to 32. An open circle is at 28. Everything to the left of the circle is shaded.

Answers

Answer:

  A number line going from negative 1 to positive 7. An open circle is at 3. Everything to the right of the circle is shaded.

Step-by-step explanation:

The area of a parallelogram is given by the formula ...

  A = bh

So, we have the condition that ...

  A > 42

  bh > 42 . . . . . substitute the expression for area

  14h > 42 . . . . fill in the given base

  h > 3 . . . . . . . divide by 14

Numbers greater than 3 are to the right of 3 on the number line.

_____

The relation is > rather than ≥, so the "or equal to" case is not included. That is why the circle is open, rather than solid.

Answer:

a).

Step-by-step explanation:

please help me with this question

Answers

Answer:  yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

A = 3

B = 5.5

C = 11

29. Find the circumference.
11
a. 3.14
b. 69.08
c. 121

Answers

Answer:

b.69.08

Step-by-step explanation:

formula:

c=2(pi)r

c=2(pi)11

Answer:b

Step-by-step explanation:

radius=r=11

π=3.14

Circumference=2 x π x r

Circumference=2 x 3.14 x 11

Circumference=69.08

What is the volume of a right circular cylinder with a radius of 5 cm and a height of 12 cm?
Unit Te
4.05 Unit
EN OP
60 cm
120 cm
3007 cm
12007 cm

Answers

Answer:742 cm^3

Step-by-step explanation:

Height=h=12cm

Radius=r=5cm

π=3.14

volume of cylinder=π x r^2 x h

Volume of cylinder=π x r x r x h

Volume of cylinder=3.14 x 5 x 5 x 12

Volume of cylinder=742 cm^3




Aiden wanted to model -15 + 15 = 0 on the number line. He first drew an arrow 15 units long starting from zero that pointed to the left. He then draws another arrow 15 units long starting from zero that points to the right. What error did Aiden make?
A. The first arrow he drew should have pointed to the right to represent -15.
B. The second arrow he drew should have pointed to the left to represent 15.
C. The first arrow he drew should have started at -15 instead of 0.
D. The second arrow he drew should have started at -15 instead of 0.

Answers

Answer:

I think it's D

Step-by-step explanation:

The number never goes over 0 so there is no need to put anything above 0

Answer:

the answer is D. The second arrow he drew should have started at -15 instead of 0.

Step-by-step explanation:

was on a test I took and got 100

A recent survey showed 3 out of 65 Happy Meals contained a “special” prize. How many “special” prizes should a person expect to win if 130 Happy Meals were purchased?

Answers

Answer:

6

Step-by-step explanation:

The ratio would be 3:65, so to get it to ?:130 you would multiply by 2 (65•2=130). So all you have to do is do 3•2=6 to get the correct ratio which is 6:130. So that answer would be 6.

The average mark of c
andidates in an aptitude test was 128.5 with a standard deviation of

8.2. Three scores extracted from the test are; 148, 102, 152. What is the average of the

extracted scores that are extreme values (outliers)?​

Answers

Answer:

The average of the extracted scores that are extreme values (outliers) = 102

Step-by-step explanation:

With the logical assumption that the population size is large enough, for a normal distribution,

68% of the data lies within 1 standard deviation of the mean.

95% of the data lies between 2 standard deviations of the mean.

99.7% of the data lies within 3 standard deviations of the mean.

So, the outliers for a normal distribution are usually beyond 3 standard deviations of the mean.

The mean = 128.5

Standard deviation = 8.2

The range of scores within 3 standard deviations of the mean is obtainable thus

(Mean ± 3standard deviations)

3 × standard deviations = 3 × 8.2 = 24.6

(128.5 ± 24.6) = (103.9, 153.1)

The 3 extracted scores are 148, 102 and 152. The only extreme value of these 3 extracted scores is 102. The two other scores are within the range of 3 standard deviations of the mean.

Hence, the average of the extracted scores that are extreme values (outliers) = 102

Hope this Helps!!!

help ASAP! giving BRAINLIEST if awnsered correctly!​

Answers

Answer:

C. (5x + 6) (5x - 6)

Step-by-step explanation:

25 is a perfect square, meaning its two factors are identical (5), and 36 is also a perfect square with two identical factors (6). With this information, we can split the expression below like this:

[tex]25x^2 - 36\\(5x ) (5x )[/tex]

Since 36 is negative, we have to have a positive 6 and a negative 6:

(5x - 6) (5x + 6)

what is the sum of this arithmetic series? 586+564+542+...+212

Answers

Answer:

Basically it's asking for the sum of 212 + 216 + 220 + ..... 586

Each number is 22 more than the previous one.

Therefore the sum will be 212 + (212+22) + (212+22*2) + (212+22*3)

the amount of numbers from 212 through 586 is 18.

Therefore we will need 212 plus 212 * 17 = 3,816 *******************

We will also need all those 22's.

We must add 22 *1 plus 22*2 plus 22*3 ..... plus 22*17

Which equals 22 + 44 + 66 + 88 ... 374

Which totals 3,366 *****************

So, we total 3,816 + 3,366 which equals 7,182

Step-by-step explanation:

 

[tex]\displaystyle\bf\\Sum=586+564+542+...+212\\\\Sum=212+234+256+...+586\\\\\textbf{We calculate the number of terms (n):}\\\\n=\frac{586-212}{22}+1=\frac{374}{22}+1=17+1=18\\\\\boxed{\bf~n=18~terms}\\\\Sum=\frac{n(586+212)}{2}\\\\Sum=\frac{18\times 798}{2}\\\\Sum=9\times798\\\\\boxed{\bf~Sum=7182}[/tex]

 

line s has a slope of 2/5. line t is perpendicular to s. what is the slope of line t​

Answers

Answer:

-5/2

Step-by-step explanation:

In order to find the slope of a perpendicular line: negate the reciprocal of the original slope

A mirror frame in the shape of an oval is shown below. The ends of the frame form semicircles: (5 points)

An oval is formed by a rectangle with semicircles at each end. The length of the rectangle is 62 inches. The width of the rectangle is 27 inches.
Which of the following is the perimeter of the inner edge of the frame?

Answers

Answer:

696.265 inches

Step-by-step explanation:

Radius = 27/2 = 13.5

2 semicircles + 2 lengths

(3.14 × 13.5²) + 2(62)

696.265 inches

Answer:

696

Step-by-step explanation:

Kevin goes to the grocery store and buys a box of cereal, a family size box of cereal, a candy bar, and a king sized candy bar. He notices that the family sized box of cereal is twice as big as the regular box of cereal and the king size candy bar is twice as big as the regular candy bar. Kevin believes that because the family sized box of cereal and king sized candy bar are twice the size that the volume is also twice the size. Is Kevin correct in his thinking?

Answers

Yes, he is thinking correctly.

Find the equation of the line that has the given properties. Write the equation in slope-intercept form, if possible.


Contains (3, 3); perpendicular to the line y = 2x - 1

Answers

Answer:

y = (-1/2)x + 9/2

Step-by-step explanation:

the equation of a straight line can be written as;

y = mx + c ......1

Where;

m = slope

c = intercept

For two lines to be perpendicular their slope must be opposite reciprocal of each other.

m1 × m2 = -1 .....2

Given;

The equation Contains (3, 3); and perpendicular to the line y = 2x - 1

Slope of the given equation m1 = 2

Slope of the line m2; substituting m1 to equation 2.

2 × m2 = -1

m2 = -1/2

So,

y = (-1/2)x + c

To solve for c, let's substitute the given point on the line; (3,3).

3 = (-1/2)(3) + c

3 = -3/2 + c

c = 3 + 3/2

c = 9/2

Therefore, the equation of the line that has the given properties is;

y = (-1/2)x + 9/2

Help ! I don’t know if I have it correct. Can somebody check it out. I got 81/65536 which I know has to be incorrect.

Answers

Answer:  9

Work Shown:

In the numerator, we have 2^2*x^2, which is really just 4x^2. Replace x with 3 and we get 4*x^2 = 4*3^2 = 36.

For the denominator, xy^2, we get

x*y^2 = 3*2^2 = 12

So far we have,

[tex]\frac{2^2x^2}{xy^2} = \frac{4x^2}{xy^2} = \frac{36}{12} = 3\\\\\text{ or simply} \\\\\frac{2^2x^2}{xy^2} = 3[/tex]

when x = 3 and y = 2.

Square both sides to end up with...

[tex]\frac{2^2x^2}{xy^2} = 3\\\\\left(\frac{2^2x^2}{xy^2}\right)^2 = 3^2\\\\\left(\frac{2^2x^2}{xy^2}\right)^2 = 9[/tex]

5×60=5×___tens
=_____tens
=______

Answers

Answer:

300

Step-by-step explanation:

5x60=5x6 tens it equal to 30 tens. 30 tens equals 300

Answer:

see below

Step-by-step explanation:

there are 6 tens in 60!

5x60 = 5 x 6 tens

= 30 tens

= 300

Solve 20x = 10 for x. A. x = 1/2 B. x = 1.5 C. x = 2 D. x = 10

Answers

Answer:

A. 1/2

Step-by-step explanation:

20x=10

Divide 20 on both sides of the equation to get x by itself

20x=10

___.  __

20.     20

x =1/2

Answer:

A) x= 1/2

Step-by-step explanation:

20x= 10 we then divide 10 by 20 to get x= 10/20 or if we simplify x= 1/2. Thus answer choice A) is correct!

A national survey of companies included a question that asked whether the customers like the new flavor of a cola from company A. The sample results of 1000 customers, and 850 of them indicated that they liked the new flavor. The 98% confidence interval on the population proportion of people who like the new flavor is _______________.

Answers

Answer:

The 98% confidence interval on the population proportion of people who like the new flavor is (0.8237, 0.8763).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 1000, \pi = \frac{850}{1000} = 0.85[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.85 - 2.327\sqrt{\frac{0.85*0.15}{1000}} = 0.8237[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.85 + 2.327\sqrt{\frac{0.85*0.15}{1000}} = 0.8763[/tex]

The 98% confidence interval on the population proportion of people who like the new flavor is (0.8237, 0.8763).

A cube with side length mmm has a volume of 343343343 cubic centimeters. The following equation shows the volume of the cube.
m^3 = 343m
3
=343m, cubed, equals, 343
What is the side length of the cube in centimeters?

Answers

Answer:7cm

Step-by-step explanation:

m^3=343

Take the cube root of both sides

m=7

Solve (x + 6)2 = 64.

Answers

Answer:

x=26

Step-by-step explanation:

(x+6)2=64

x+6=32

x=26

Answer:

Here is the solution. Mark as brainlist please.

Natalia paid $38.95 for three medium-sized pizzas and a salad. If Natalia paid $11 for the salad, how much did each pizza cost? Enter your answer in the box.

Answers

Answer:

$9.32

Step-by-step explanation:

If she paid $11 for the salad, then the three pizzas cost 38.95 - 11.00 which is 27.95.  Divide that by three and you get $9.32 (if you round to the nearest penny)

What type of triangle is shown in the image?


Acute triangle
Right triangle
Equilateral triangle
Obtuse triangle

Answers

The triangle is an Obtuse triangle

The type of triangle shown in the image is the Obtuse triangle.

What is an obtuse triangle?

A triangle is said to be an obtuse triangle if one of its angles measures more than 90 degrees.

In the given diagram, one of the angles measures more than 90 degrees.

So, the given triangle is an obtuse triangle.

Hence, the type of triangle shown in the image is the Obtuse triangle.

To get more about obtuse triangles visit:

https://brainly.com/question/5023725

The number 65 is decreased to 62. What is the percentage by which the number was decreased, to the nearest tenth of a percent?

Answers

Answer:4.6

Step-by-step explanation:

Percentage decrease=(65-62)/65 x 100

Percentage decrease=3/65 x 100

Percentage decrease=(3x100)/65

Percentage decrease=300/65

percentage decrease=4.6

Please help ASAP! I will mark BRAINLIEST! Please answer CORRECTLY! No guessing! CHECK ALL THAT APPLY

Answers

Answer:

D. 96

F. 32

Step-by-step explanation:

The inequality 3x ≥ 96, means that x and 3 must be multiplied to get a product that is greater than 96.  So to figure this out, you must plug in the numbers given for x, like so:

3x ≥ 96

A. 3(31) ≥ 96

     93 ≥ 96                            This is incorrect since 93 is not greater than 96

A tip that makes this easier is that, you can see that 31 multiplied by 3 is 93, which is only a couple numbers off 96, so all numbers after 31 will result in a product greater than 96. For example:

D. 3(96) ≥ 96

    288 ≥ 96                             This inequality is correct

F. 3(32) ≥ 96

   96 ≥ 96                        

The inequality sign states that the number must be either greater or equal to 96, which it is.

Sam conducted a survey to determine your favorite flavor of ice cream is his hometown. 15 of the 50 people he surveyed liked strawberry best. How many of the 3,500 residents in the town would you expect to like strawberry best

Answers

Answer: 1050 people.

Step-by-step explanation: It's a rule of three question.

15/50 as x/3500

Then you have that 50x = 52500

x = 1050

There you have it.

Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.

Answers

Answer:

A. X=6 only

Step-by-step explanation:

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