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2 years ago

Please help don’t understand

Mathematics

1 answer:

sergejj [24]2 years ago

8 0

Answer:

x=35

Step-by-step explanation:

2x+15+2x-10+x=180

combine factors

5x+5=180

-5 from both sides

5x=175

divide 175/5x

x=35

You might be interested in

If the length of each side of an equilateral triangle were increased by 50 percent, what would be the percent increase in the ar

Shkiper50 [21]

Answer:

The area increase by 225%

Step-by-step explanation:

attachment of a triangle

The area of a triangle equilateral is calculated with the next formula:

A= $\frac{a*h}{2}$

$h^{2} +(\frac{a}{2})^{2}$ = $a^{2}$

$h^{2} = a^{2} - \frac{a^{2} }{4}$ = $\frac{a^{2} }{4}$ *3

h= $\sqrt{\frac{a^{2}*3 }{4} }$

h= $\frac{\sqrt{3}*a }{2}$

replacing in the A equation:

A= $\frac{a*\sqrt{3}*a }{2*2}$ 

A= $\frac{\sqrt{3}*a^{2} }{4}$ 

Now each side increse by 50% ⇒ a=1.5a

A= $\frac{\sqrt{3}*(1.5a)^{2} }{4}$ 

A= $\frac{\sqrt{3}*a^{2}* 2.25 }{4}$ 

A=2.25 * $\frac{\sqrt{3}*a^{2} }{4}$ 

It means that the area incrase by 225%

6 0

3 years ago

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}

n = 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 t confidence interval.

The critical value of t 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 t-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

0 2. What is the area of a rectangle with a width of 6.5 feet and a length of 14 feet?

photoshop1234 [79]

Answer:

Area=91 ft^2

Step-by-step explanation:

Area=length*width

Area= 14*6.5

Area=91 ft^2

5 0

3 years ago

A point P is moving along the curve whose equation is y = \sqrt x . Suppose that x is increasing at the rate of 4 units/s when x

Mice21 [21]

Answer:3 units/s

Step-by-step explanation:

Given

$y=\sqrt{x}$

Point P lie on this curve so any general point on curve can be written as $(x,\sqrt{x})$

and $\frac{\mathrm{d} x}{\mathrm{d} t}=4 units/s$

Distance between Point P and (2,0)

$P=\sqrt{(x-2)^2+(\sqrt{x}-0)^2}$

P at x=3 P=2

rate at which distance is changing is

$\frac{\mathrm{d} P}{\mathrm{d} t}=\frac{\mathrm{d} \sqrt{(x-2)^2+(\sqrt{x}-0)^2}}{\mathrm{d} t}$

$\frac{\mathrm{d} P}{\mathrm{d} t}=\frac{2x-3}{\sqrt{(x-2)^2+(\sqrt{x}-0)^2}}\times \frac{\mathrm{d} x}{\mathrm{d} t}$

$\frac{\mathrm{d} P}{\mathrm{d} t}=\frac{2\times 3-3}{2\times 2}\times 4=3 units/s$

8 0

3 years ago

25x^2+1=5 quadratic

Olenka [21]

25x² + 1 = 5

25x² + 1 - 5 = 0

25x² - 4 = 0 By difference of two squares

(5x)² - (2)² = 0

(5x - 2)(5x + 2) = 0

5x - 2 = 0 or 5x + 2 = 0

5x = 0 + 2 5x = 0 - 2

5x = 2 5x = -2

x = 2/5 x = -2/5

x = 0.4 x = -0.4

x = + 0.4 or -0.4

3 0

3 years ago