A smartphone costs $280. sales tax is 5%. What is the total cost,including tax?

Answer:

3

Step-by-step explanation:

logb(8)

logb(2³)

3 × logb(2)

3 × 1

3

Answer:

7/4

Step-by-step explanation:

We know that US = RU, so we can just set those expressions equal to each other.

US = 3m + 2

RU = -m + 9

US = RU  ⇒  3m + 2 = -m + 9  ⇒  4m = 7  ⇒  m = 7/4

Hope this helps!

Answer:

7/4 or 1¾

Step-by-step explanation:

Since US = UR

3m + 2 = -m + 9

4m = 7

m = 7/4

m = 1¾

Answer and Step-by-step explanation:

Since this is a quadrilateral, we know that all the angles will add up to 360 degrees (by definition). We are given that angle A is 90 degrees and that the ratio of A to B is 5 to 3. This means that we can set up a proportion and solve for B:

A/B = 5/3  ⇒  90/B = 5/3  ⇒  5B = 270  ⇒  B = 54

So, we know that angle B is 54 degrees.

Now that we know angle B is 54 and A is 90, we can find the sum of the remaining two angles X and Y because A + B + X + Y = 360:

90 + 54 + X + Y = 360

X + Y = 216 degrees

We also know that the ratio of X to Y is 1 to 3, so we can set up another proportion:

X/Y = 1/3  ⇒  Y = 3X

Substitute 3X in for Y in X + Y  = 216:

X + 3X = 216

4X = 216

X = 54

Thus, we see that both angles B and X equal 54, so B = X.

Hope this helps!

Answer:

[tex]\frac{a}{b}=\frac{5}{3}=>b=\frac{3a}{5}=\frac{270}{5}=54 \\\\x+y=360-(90+54)=360-144=216\\\\\frac{x}{y}=\frac{1}{3}=>y=3x\\ \\x+3x=216\\\\4x=216\\\\x=216:4\\\\x=54\\\\x=b\\[/tex]

Slope-intercept form: [tex]y=mx+b[/tex]

Slope formula: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We're given:

1) First, find the slope using the slope formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{8-(-9)}{6-3}\\\\m=\dfrac{8+9}{6-3}\\\\m=\dfrac{17}{3}[/tex]

Therefore, the slope of this line (m) is [tex]\dfrac{17}{3}[/tex]. Plug this into slope-intercept form:

[tex]y=\dfrac{17}{3}x+b[/tex]

2) Now, find the y-intercept by using one of the given points:

[tex]y=\dfrac{17}{3}x+b[/tex]

Plug in one of the given points as (x,y):

[tex]8=\dfrac{17}{3}(6)+b\\\\8=34+b\\b=8-34\\b=-26[/tex]

Therefore, the y-intercept of the line is -26. Plug this into our original equation:

[tex]y=\dfrac{17}{3}x+b\\\\y=\dfrac{17}{3}x-26[/tex]

[tex]y=\dfrac{17}{3}x-26[/tex]

To write the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept, we need to determine the slope first and then use one of the points to find the y-intercept.

Step 1: Find the slope (m)
The slope of a line passing through two points, (x1, y1) and (x2, y2), can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

Given our points (6, 8) and (3, -9), we can substitute them into our formula:

x1 = 6, y1 = 8
x2 = 3, y2 = -9

m = (-9 - 8) / (3 - 6)
m = (-17) / (-3)
m = 17/3
m = 5.666666666666667 (rounded to 5.67 for simplicity)

Step 2: Find the y-intercept (b) using one of the points
Next, we can use the point-slope form of a line equation, which is:

y - y1 = m(x - x1)

We will use the first point (6, 8) and the slope m = 5.67 that we calculated.

Substitute the point and the slope into the point-slope form equation:

8 - y1 = 5.67(6 - x1)

Since we know that (x1, y1) is (6, 8), this simplifies to:

8 - 8 = 5.67(6 - 6)
b = 8 - 5.67(6)

Now, we do the multiplication and subtraction:

b = 8 - 34.02
b = -26

So now we have our y-intercept, which is b = -26.

Step 3: Write the equation in slope-intercept form
Now that we have both m and b, we can write the equation of the line:

y = mx + b

Substitute m and b into the equation:

y = 5.67x - 26

This is the equation of the line in slope-intercept form that passes through the points (6, 8) and (3, -9). For exact calculations, you may want to use the more precise value of the slope (5.666666666666667) in the equation:

y = 5.666666666666667x - 26

By doing so, we obtain a more accurate representation of the line's equation.

Answer:

487.5 miles

Step-by-step explanation:

The actual distance between the cities is 487.5 miles.

Two or more ratios made to be equivalent to each other is termed as the method of proportion.

That is, if 'a' related to 'b' is proportional to 'p' related to 'q', then,

a : b : : p : q

⇒ a/b = p/q

⇒ aq = bp

Here we have the scale on a map reads 1/2 inch as 75 miles.

We have to find the actual distance of two cities if the distance between the cities in the map is 3 and 1/4 inches.

3 and 1/4 inches = (3 × 4 + 1) / 4 = 13/4 inches.

Let x be the actual distance between the cities.

Using proportion,

1/2 : 75 : : 13/4 : x

[tex]\frac{1/2}{75}[/tex] = [tex]\frac{13/4}{x}[/tex]

1/2 × x = 13/4 × 75

1/2 × x = 243.75

x = 487.5

Hence the actual distance between the cities is 487.5 miles.

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Answer:

There will be one person on 1 square yard of land after 1,892,147.588 years.

Step-by-step explanation:

Continuous exponential growth formula:

[tex]P(t)=Pe^{rt}[/tex]

P(t)= Population after t years.

P= Initial population

r=rate of growth.

t= time in year

Given that,

Growth rate of country A (r)= 4.9% per year=0.049 per year.

Initial population (P)= 151,000.

Land area of country area= 14,000,000,000 square yards.

There will be one person on one  square yard of land.

So, there will be 14,000,000,000  person for 14,000,000,000 square yard of land in country A.

P(t)=14,000,000,000 person

[tex]\therefore 14,000,000,000= 151,000 e^{0.049t}[/tex]

[tex]\Rightarrow e^{0.049t}=\frac{ 14,000,000,000}{ 151,000}[/tex]

Taking ln both sides

[tex]\Rightarrow ln|e^{0.049t}|=ln|\frac{ 14,000,000,000}{ 151,000}|[/tex]

[tex]\Rightarrow {0.049t}=ln|\frac{ 14,000,000,000}{ 151,000}|[/tex]

[tex]\Rightarrow t}=\frac{ln|\frac{ 14,000,000,000}{ 151,000}|}{0.049}[/tex]

[tex]\Rightarrow t}=1,892,147.588[/tex] years

There will be one person for every square yard of land after 1,892,147.588 years.

Answer:

D. -6.

Step-by-step explanation:

The inverse is the number when added to 6  results in 0.

So it is 0 - 6 = -6.   (6 + -6 = 0)

Answer:

C

Step-by-step explanation: I big brain

Answer:16

Step-by-step explanation:AC is half of ED

Answer:

9

Step-by-step explanation:

To find the common ratio, take the second term and divide by the first

36/72 = 1/2

To find the next term, take the last term and multiply by the common ratio

18*1/2 = 9

Answer:

9.

Step-by-step explanation:

The common ratio = 36/72 = 18/36 = 1/2.

So the next term is 18 * 1/2 = 9.

[tex](x - 17.7) + 19.6 = 27.8 \\ x - 17.7 = 27.8 - 19.6 \\ x - 17.7 = 8.2 \\ x = 17.7 + 8.2 \\ x = 25.9[/tex]

The scale of the drawing to the new barn is 1:1.5.

To find the scale of the new barn compared to the existing barn, we can use the ratio of their sides. Let's call the shortest side of the new barn x meters. The ratio of the lengths of the shortest sides of the new and existing barns is given as 2/3. Setting up the proportion, we have 2/3 = x/150. Cross-multiplying, we find x = (2/3) * 150 = 100 meters. Therefore, the shortest side of the new barn measures 100 meters. The scale of the drawing to the new barn can be determined by dividing the length of the shortest side of the drawing by the length of the shortest side of the new barn. Let's call the scale factor y. We have y = 150/100 = 1.5. Therefore, the scale of the drawing to the new barn is 1:1.5.

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Answer:

Step-by-step explanation:

The Venn diagram representing this situation is shown in the attached photo.

P represents the set of college graduates that donated to a political campaign.

M represents the set of college graduates that donated to assist medical research.

E represents the set of college graduates that donated to preserve the environment.

From the diagram,

The number of college graduates that donated to all three is 25

The number of college graduates that donated to a political campaign and medical research only is

38 - 25 = 13

The number of college graduates that donated to a political campaign and preserve the environment only is

54 - 25 = 29

The number of college graduates that donated to medical research and to preserve the environment only is 46 - 25 = 21

The number of college graduates that donated to a political campaign only is

95 - (29 + 25 + 13) = 28

The number of college graduates that donated to medical research only is

76 - (13 + 25 + 21) = 17

The number of college graduates that donated to preserve the environment only is

133 - (29 + 25 + 21) = 58

a) the number of college graduates that donated to none is

489 - (28 + 17 + 58 + 13 + 21 + 29 + 25)

= 298 college graduates

b) the number of college graduates that donated to exactly one of the three listed causes is

28 + 17 + 58 = 103

The percentage would be

103/489 × 100 = 21.1%

Answer:

46 feet

Step-by-step explanation:

Perimeter of rectangle needed =

[tex]14+14+7= 35\\[/tex]

Half of the circumference of a circle needed =

[tex]\frac{1}{2} \pi d = \frac{1}{2} * \frac{22}{7} * 7= 11[/tex]

Total perimeter needed =

[tex]35 + 11=46[/tex]

Answer:

46 ft

Step-by-step explanation:

John will need to put a fence along 3 sides of the rectangle: 14 ft, 7 ft, 14 ft

He also needs to put a fence along the half circle:

C (circumference) = 2×π×r = π×d

⇒C÷2 = π×d÷2 = 22/7×7÷2 = 22÷2 = 11 ft

Together: 14 + 7 + 14 + 11 = 46 ft

Answer:

This depends on the way the triangle

Step-by-step explanation:

Anyway angles that apply includes: 55 and 70

He had saved 320 initially

Step-by-step explanation:

Let the amount he saved be 'a'

Amount spent = 20 + 40 + 30

= 90

His grand father gave 50

At the end he has 280

280 = a - 90 +50

a = 280 -50 +90

= 320

He had saved 320 initially

Answer:

$40.05

Step-by-step explanation:

You would add up 2.70+15.45+22.90 then, subtract the total by 1.00

Answer:

40.05

Step-by-step explanation:

you basically add up all the prices then subtract the 1 dollar the he has and u get ur answer

Answer:

Scale factor = 1/2

Ratio R:T = 2:1

Attached is the missing image;

Step-by-step explanation:

From the image attached;

The height of the triangle T is = 5 units

Base of triangle T = 4 units

Since the two triangles are scaled versions;

Area of a triangle = 1/2 × h × b

For triangle R;

Area = 40 = 1/2 × h × b

hb = 80

And, h : b = 5:4

h= 5/4 b

5/4 ×b × b = 80

b^2 = 64

b = 8

h = 5/4 × 8 = 10

The height of the triangle R = 10 units

Base of triangle R = 8 units

Scale factor = h2/h1 = 5/10 = 1/2

Scale factor = 1/2

Answer:

The 95% confidence interval has Minimum = 6.053 and Maximum = 7.467

Step-by-step explanation:

Here we have

Data as

1 5 6 7 8 8 8 9 9 9 9 10 3 4 5 5 7 6 8 9 10 5 4 6 5 7 3 1 9 8 8 9 9 10 7 6 4 8 10 2 5 1 8 6 9 6 8 8 10 10

The sum is 338

∴ Mean, [tex]\bar x[/tex] = 6.76, Standard Deviation, s = 2.55

Sample size, n = 50

For a 95% confidence interval, we have

[tex]CI=\bar{x}\pm z\frac{s}{\sqrt{n}}[/tex]

Where z is;

z at 95% z = [tex]\pm[/tex]1.96

Therefore, we have

95% confidence interval as Minimum = 6.053 to Maximum = 7.467.

Answer:

79 years old

Step-by-step explanation:

Let's say your age is x.

The problem says "500 reduced by 4 times my age is 184", so we convert this to math:

- "4 times my age" ⇒ 4 * x = 4x

- "500 reduced by" ⇒ 500 - (something)

- "500 reduced by 4 times my age" ⇒ 500 - 4x

- "is 184" ⇒ = 184

- "500 reduced by 4 times my age is 184" ⇒ 500 - 4x = 184

Now, we simply solve for x:

500 - 4x = 184

4x = 500 - 184 = 316

x = 79

Thus, you are 79 years old.

Hope this helps!

Answer:

The distance between them is 366.75 feet.

She doesn't need to sound a warning yet.

Step-by-step explanation:

Please see the attached files for explanation.

To find the Distance between ships, we can use trigonometry. The distance between the ships is the absolute difference between their heights above the horizontal.

To find the distance between the two ships, we can use trigonometry. Let's consider the triangle formed by the lighthouse, ship 1, and ship 2. The angle of depression to ship 1 is 20°, so the angle between the line of sight and the horizontal is also 20°. Similarly, the angle of depression to ship 2 is 12.5°, so the angle between the line of sight and the horizontal is also 12.5°.

We can use the tangent function to find the height of ship 1 and ship 2 above the horizontal. Using the formula tan(angle) = opposite/adjacent, we have: tan(20°) = height of ship 1/208 and tan(12.5°) = height of ship 2/208. Rearranging these equations, we get the heights: height of ship 1 = 208 * tan(20°) and height of ship 2 = 208 * tan(12.5°).

Now, to find the distance between the ships, we need to subtract the heights of the ships from each other. If the distance is less than 300 feet, the keeper will sound a warning. So, the distance between the ships is: distance = |height of ship 1 - height of ship 2|. If this distance is less than 300 feet, she will sound the warning.

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Answer:

D. Both data sets have the same number of data points.

Step-by-step explanation:

Answer:

itd d on egeunity

Step-by-step explanation:

Answer:

[tex]\frac{\pi }{6}[/tex]

Step-by-step explanation:

[tex]\frac{\pi}{180}[/tex] = [tex]\frac{x}{30}[/tex]

180x = 30π

x = [tex]\frac{30\pi }{180}[/tex]

x = [tex]\frac{3\pi }{18}[/tex]

x= [tex]\frac{\pi}{6}[/tex]

Answer:

15

Step-by-step explanation:

Hello!

To find the median, all you have to do is order the number of terms in ascending order and then count to the middlemost number(s).

Arranging in ascending order:

[tex]6,\:12,\:14,\:15,\:15,\:18,\:19,\:19[/tex]

Since this is an even number, our two medians are 15 and 15.

(15 + 15) / 2 = 15.

Thus, the median of successful free throws is [tex]\boxed{15}[/tex].

Answer:

y=−259x+8

Step-by-step explanation:

i think this might be the answer but not sure

Answer:D

Step-by-step explanation:

10 cards would have 5 even cards.

First pick would be 5/10 = 1/2 probability of getting an even card.

Without replacing there are 9 cards left with 4 even ones. The probability of picking an even card would be 4/9

The probability of both happening would be Found by multiplying the two probability’s together:

1/2 x 4/9 = 4/18 = 2/9

Two cards are selected from a deck of cards numbered from [tex]1[/tex] to [tex]10[/tex] and once a card is selected, it is not replaced, then Probability of two even numbers is [tex]\frac{2}{9}[/tex] .

Probability is a ratio of the number of favorable outcomes to the number of possible outcomes of the experiment.

Probability[tex](E)[/tex] [tex]=\frac{Number \ of \ favorable \ outcomes}{Number \ of \ possible \ outcomes \ of \ the \ experiment}[/tex]

We have,

Let [tex]E[/tex] be event of drawing cards.

A deck of cards numbered from [tex]1[/tex] to [tex]10[/tex] .

i.e. total number of possible outcomes [tex]=10[/tex]

And,

Even numbers from [tex]1[/tex] to [tex]10[/tex]  are [tex]2,4,6,8,10[/tex]

[tex]=10[/tex]

Total even numbers are [tex]5[/tex].

So,

Probability[tex](E)[/tex] [tex]=\frac{Number \ of \ favorable \ outcomes}{Number \ of \ possible \ outcomes \ of \ the \ experiment}[/tex]

Probability[tex](E)[/tex] [tex]=\frac{5}{10}*\frac{4}{9}[/tex]

                           [tex]=\frac{2}{9}[/tex]

So, the Probability of two even numbers is [tex]\frac{2}{9}[/tex] , as there are total [tex]10[/tex] cards and it is said that once a card is selected, it is not replaced, so when one card is selected there remains only [tex]9[/tex] cards, so when next time we select a card then Probability will be from those [tex]9[/tex] cards.

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The angle subtended by an arc [tex]\widehat{AU}[/tex] is given by the angle ∠UOA.

Response:

According to circle theorem, we have;

∠QUA = 111°

Therefore;

[tex]m\widehat{QDA}[/tex] = 2 × ∠QUA

[tex]m\widehat{QDA}[/tex] = 2 × 111° = 222°

Which gives;

Angle ∠QOA = [tex]m\widehat{QUA}[/tex] = 360° - 222° = 138°

∠QOA = ∠QOU + ∠UOA by angle addition property

Which gives;

∠QOA = 138° = 88° + ∠UOA

∠UOA = 138° - 88° = 50°

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The mean is 59

Add all the scores together, then divide by the number of test scores

The mean of the scores to the nearest 10th Score Number of Students is 59.

We have given a data,

80,85,6,90,95,100,6,8

Mean is the adding all the scores together, then divide by the number of test scores.

So we have given a data,

80,85,6,90,95,100,6,8

80+85+6+90+95+100+6+8=470

The number of of test scores=8

[tex]mean=\frac{470}{8}=58.75[/tex]

Mean≈59

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Answer:

so f(0) = g(0)   and f(2) = g(2)

Step-by-step explanation:

f(x) = g(x) where the two graphs intersect

The graphs cross at the x coordinate 0  and x coordinate 2

so f(0) = g(0)   and f(2) = g(2)

Answer:

First one

Step-by-step explanation:

f(x) = g(x)

Is the point of intersection of the two graphs

(0,4) and (2,0)

Solutions are: x = 0 and x = 2

Answer:

[tex]\£465.31[/tex]

Step-by-step explanation:

we know that

The insurance company reduces the price by 2.1%

Remember that

The actual cost of £475.29 a year represent the 100%

so

[tex]100\%-2.1\%=97.9\%=97.9/100=0.979[/tex]

To find out the new insurance cost, multiply the original cost by the factor 0.979

[tex]\£475.29(0.979)=\£465.31[/tex]

Brian's car insurance, after a 2.1% reduction from the original cost of £475.29, is now £465.31 when rounded to two decimal places.

Brian's original car insurance cost is £475.29, and the company is offering a reduction of 2.1% on this cost. To calculate the reduced cost, we first find the discount amount by multiplying the original cost by the reduction percentage:

Discount = Original Cost x Reduction Percentage

Discount = £475.29 x 0.021

Discount = £9.98109

Now, we subtract the discount from the original cost to find the new cost of the insurance:

New Cost = Original Cost - Discount

New Cost = £475.29 - £9.98109

New Cost = £465.30891

When rounding to two decimal places, Brian's new cost for car insurance is:

New Cost = £465.31

Answer:

C.1/6

Step-by-step explanation: