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scZoUnD [109]
3 years ago
9

Algebra: Find x ....

Mathematics
1 answer:
luda_lava [24]3 years ago
3 0

Answer:

d

Step-by-step explanation:

The triangles are similar, thus the ratios of corresponding sides are equal, that is

\frac{2x+1}{x+4} = \frac{40}{25} = \frac{8}{5} ( cross-  multiply )

5(2x + 1) = 8(x + 4) ← distribute parenthesis on both sides )

10x + 5 = 8x + 32 ( subtract 8x from both sides )

2x + 5 = 32 ( subtract 5 from both sides )

2x = 27 ( divide both sides by 2 )

x = 13.5 → d

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Connecticut families were asked how much they spent weekly on groceries. Using the following data, construct and interpret a 95%
Amanda [17]

Answer:

The 95% confidence interval for the population mean amount spent on groceries by Connecticut families is ($73.20, $280.21).

Step-by-step explanation:

The data for the amount of money spent weekly on groceries is as follows:

S = {210, 23, 350, 112, 27, 175, 275, 50, 95, 450}

<em>n</em> = 10

Compute the sample mean and sample standard deviation:

\bar x =\frac{1}{n}\cdot\sum X=\frac{ 1767 }{ 10 }= 176.7

s= \sqrt{ \frac{ \sum{\left(x_i - \overline{x}\right)^2 }}{n-1} }       = \sqrt{ \frac{ 188448.1 }{ 10 - 1} } \approx 144.702

It is assumed that the data come from a normal distribution.

Since the population standard deviation is not known, use a <em>t</em> confidence interval.

The critical value of <em>t</em> for 95% confidence level and degrees of freedom = n - 1 = 10 - 1 = 9 is:

t_{\alpha/2, (n-1)}=t_{0.05/2, (10-1)}=t_{0.025, 9}=2.262

*Use a <em>t</em>-table.

Compute the 95% confidence interval for the population mean amount spent on groceries by Connecticut families as follows:

CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot\ \frac{s}{\sqrt{n}}

     =176.7\pm 2.262\cdot\ \frac{144.702}{\sqrt{10}}\\\\=176.7\pm 103.5064\\\\=(73.1936, 280.2064)\\\\\approx (73.20, 280.21)

Thus, the 95% confidence interval for the population mean amount spent on groceries by Connecticut families is ($73.20, $280.21).

7 0
3 years ago
I NEED HELP WITH THIS ASAP THIS IS PART OF MY GRADE (no its not lol) THIS IS SOOO HARD CAN YOU ANSWER 2-2+2 OMG ITS HARD RIGHT??
OlgaM077 [116]
The answer is 2, OMG IT IS HARDDDDDDD
4 0
3 years ago
Read 2 more answers
Can someone help me find the value of z? ⅔z + 1 = 13
sergey [27]

Answer:

z = 18

Step-by-step explanation:

Given: ⅔z + 1 = 13

Subtract one from both sides: ⅔z = 12

Multiply both sides by the inverse of 2/3, which is 3/2: z = 18

Have a nice day!

    I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

4 0
2 years ago
(3) Two people are at an elevator. At the same time one person starts to walk away from the elevator at a rate of 2 ft/sec and t
Gekata [30.6K]

Answer:

The rate at which the distance between the two people is changing 15 seconds later is 7.28 ft/sec.

Step-by-step explanation:

Here, we note the following

Let the person walking way fom the elevator be X

Let the other person going up in the elevator be Y

Therefore after 15 seconds, their positions will be;

For X,  2 ft/sec × 15 s = 30 ft away from the elevator

For Y,  7 ft/sec × 15 s = 105 ft up in the elevator

At that instant, the distance between them is given as

d² = x² + y²

= 30² +105² = 11925 ft²

d = √11925 ft²  = 109.202 ft

The rate of change of the distance between the two peopl, X and Y is given as

\frac{dd^2}{dt} = \frac{dx^2}{dt} + \frac{dy^2}{dt}

Therefore,  2d\frac{dd}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt} or d\frac{dd}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}

Since \frac{dx}{dt} is given as 2 ft/sec and \frac{dy}{dt} = 7 ft/sec

Then  d\frac{dd}{dt} = 30 \times 2 + 105 \times 7 = 795\\

\frac{dd}{dt} = \frac{795}{109.202 } =7.28 ft/sec

8 0
3 years ago
Read 2 more answers
Don't Send links, don't Write random things and get the points for free.
Dahasolnce [82]

Answer:

2,714in^3

Step-by-step explanation:

V = pi*r^2*h
V = 3.14*6^2*24
V = 3.14*36*24
V = 2,714

The volume of the cylindrical fish tank is 2,714 inches cubed.

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2 years ago
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