What is the sum of the series? ​∑j=152j​ Enter your answer in the box.

Answer:

41 and 11.

Step-by-step explanation:

Let's say the 2 numbers are x and y.

Since they add up to 52, x + y = 52.

Seeing as the difference is 30, x - y = 30 assuming x is the larger number.

We have left:

x + y = 52

x - y = 30

By solving these simultaneous equations (adding the 2 equations together for instance), we are left with 2x = 82

Therefore x = 41.

Since x + y = 52

41 + y = 52

Therefore y = 11

Therefore we have: the larger number is 41 and the smaller number is 11.

Answer:

the amount of money Ian invested is P =  £2,500

Step-by-step explanation:

The standard formula for compound interest is given as;

[tex]A = P(1+r/n)^{nt} \\P = \frac{A}{(1+r/n)^{nt}} ...........1\\[/tex]

Where;

A = final amount/value

P = initial amount/value (principal)

r = rate yearly

n = number of times compounded yearly.

t = time of investment in years

For this case, Given that;

A = £2652.25

t = 2 years

n = 1 (semiannually)

r = 3% = 0.03

substituting the given values into equation 1;

[tex]P = \frac{A}{(1+r/n)^{nt}} ...........1\\P = \frac{2652.25}{(1+0.03)^{2}} \\P = \frac{2652.25}{(1.03)^{2}} \\[/tex]

P =  £2,500

the amount of money Ian invested is P =  £2,500

Answer:

When Ø = 300°, Ø = 60 degrees.

When Ø = 225°, Ø = 45 degrees.

When Ø = 480°, Ø = 60 degrees.

When Ø = -210°, Ø = 30 degrees.

Step-by-step explanation:

Reference angles are in Quadrant I (0° to 90°).

1. Find 300° (Quadrant IV) on the unit circle. Since it's in Quadrant IV, you use 360 - 300 = 60° to get your answer.

2. Find 225° (Quadrant III) on the unit circle. Since it's in Quadrant III, you use 225 - 180 = 45° to get your answer.

3. The angle 480° is not on the unit circle. To find its corresponding angle between 0° and 360°, use 480 - 360 = 120°. Then, find 120° (Quadrant II) on the unit circle. Since it's in Quadrant II, you use 180 - 120 = 60° to get your answer.

4. The angle -210° is not on the unit circle. To find its corresponding angle between 0° and 360°, use -210 + 360 = 150°. Then, find 150° (Quadrant II) on the unit circle. Since it's in Quadrant II, you use 180 - 150 = 30° to get your answer.

In general, if we have [tex]x^a=x^b,[/tex] then [tex]a=b.[/tex] Thus, the first answer choice is correct.

Answer:

[tex]\boxed{\red{2x - 1 = 5x - 14}}[/tex]

First answer is correct.

Step-by-step explanation:

we know that,

[tex] {x}^{a} = {x}^{b} [/tex]

[tex]a = b[/tex]

So, according to that,

[tex] {5}^{(2x - 1)} = {5}^{(5x - 14)} [/tex]

Therefore,

[tex]2x - 1 = 5x - 14[/tex]

Answer:

g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))

Step-by-step explanation:

Using the fundamental theorem of calculus

Taking the derivative of the integral gives back the function

Since the lower limit is a constant when we take the derivative it is zero

d/dx [tex]\int\limits^x_4 {g(t)} \, dt = g(x)[/tex]

g(t) = sinh^-1 ( ln(7t^6 +3) / sqrt( 8+cot( t^( 3+t))))

Replacing t with x

g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))

Answer:

[tex]\huge\boxed{x=\sqrt{21}}[/tex]

Step-by-step explanation:

ΔABD and ΔBCD are similar (AAA).

Therefore the corresponding sides are in proportion:

[tex]\dfrac{BD}{CD}=\dfrac{AD}{BD}[/tex]

Substitute

[tex]BD=x;\ CD=3;\ AD=7[/tex]

[tex]\dfrac{x}{3}=\dfrac{7}{x}[/tex]              cross multiply

[tex](x)(x)=(3)(7)\\\\x^2=21\to x=\sqrt{21}[/tex]

Answer:

1.9375.

Step-by-step explanation:

To solve this, we must use PEMDAS.

The first things we take care of are parentheses and exponents.

Since there are no parentheses, we do exponents.

4^-1+8^-1÷1/2/3^3​

= [tex]\frac{1}{4} +\frac{1}{8} / 1/ 2/ 27[/tex]

= 1/4 + (1/8) / 1 * (27 / 2)

= 1/4 + (27 / 8) / 2

= 1/4 + (27 / 8) * (1 / 2)

= 1/4 + (27 / 16)

= 4 / 16 + 27 / 16

= 31 / 16

= 1.9375.

Hope this helps!

Answer:

[tex]x= \frac{5^{14}+3}{2}[/tex]

Step-by-step explanation:

The correct steps to solve the equation are:

[tex]14=log_5(2x-5)[/tex]

[tex]5^{14}=5^{log_5(2x-3)}[/tex]

Because [tex]a^{log_am}=m[/tex]

So, solving we get:

[tex]5^{14}=2x-3[/tex]

Sum 3 on every side:

[tex]5^{14}+3=2x-3+3\\5^{14}+3=2x[/tex]

Dividing by 2 into both sides:

[tex]\frac{5^{14}+3}{2}=\frac{2x}{2}\\\frac{5^{14}+3}{2}=x[/tex]

So, the answer is  [tex]x= \frac{5^{14}+3}{2}[/tex]

Answer: Step 2

Step-by-step explanation:

This is correct according to Edge 2021

Answer:

vol = 96

Step-by-step explanation:

Area of a triangle = 1/2 * b * h

b = 4

h = 6

A = 0.5 * 4 * 6

A = 12

length = 8

vol = Area * length

vol = 12 * 8

vol = 96

Answer:

(104 + 16 sqrt 13)

Step-by-step explanation:

i did this on my school, it was correct

Answer: 1unit.

Step-by-step explanation:

Area of the rectangle

A = length × width

Since the area = 20 and the width is x and the length is x + 1.

We now substitute for the values in the above formula and solve for x

20 = x × x + 1

20 = x( x + 1 ), we now open

20 = x² + x , then re arrange.

x² + x - 20 = 0, this is a quadratic equation.we solve for x using quadratic means

Here, I am going to solve using factorization by grouping

x² + x - 20 = 0

x² + 5x - 4x - 20 = 0

x( x + 5 ) - 4( x + 5 ) = 0

( x + 5 )( x - 4 ). = 0

Therefore, the solution for x will be

x = -5 or 4, but x can not be -5 ( negative), so x = 4.

Now the difference between width and the length can easily be calculated from the above,

Width = 4 (x) , and length = 5 (4 + 1),

Now difference will be

5 - 4 = 1unit.

Answer:

All real numbers except for 5.

Step-by-step explanation:

[tex]f(x)=\frac{x}{x-5}[/tex]

The domain of rational functions is determined by the denominator. The denominator cannot equal zero since if they do, the function will be undefined.

Thus, we need to find the zero(s) of the denominator to determine the domain.

[tex]x-5=0[/tex]

[tex]x=5[/tex]

Therefore, the domain of the rational function is all real numbers except for 5.

In set builder notation, this is:

[tex]\{x|x\in \mathbb{R}, x\neq 5\}[/tex]

Answer:

Angle BCA = 70

Angle CAB = 20

Step-by-step explanation:

Not sure what angle you meant, so I'll give you all of them <3

Angle BCA = 70 degrees, because If two angles form a line, they add up to 180.  (110+x=180, x = 70)

Angle CAB = 20 degrees, because there are 180 degrees in a triangle, so 90+70+x=180, x = 20

Hope it helps <3

Answer:

BCA = 70

CAB = 20

ABC=90

Step-by-step explanation:

ABC is 120 because the square indicates that

BCA = 70 because angles on a straight line add up to 180.

110+x=180

x=180-110

=70

Angle CAB = 20 degrees, because angles in a triangle add up to 180

90+70+x=180

x = 180-(90+70)

=180-160

=20

Please mark as brainliest

Answer:

Type I error: Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.

Type II error: Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.

Step-by-step explanation:

We are given the following hypothesis below;

Let p = proportion of people who write with their left hand

Null Hypothesis, [tex]H_0[/tex] : p = 0.18      {means that the proportion of people who write with their left hand is equal to 0.18}

Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 0.18      {means that the proportion of people who write with their left hand is different from 0.18}

Type I error states that we would reject the null hypothesis given the fact that the null hypothesis was actually true. Or in other words, the probability of rejecting a true hypothesis.

So, according to our question, Type I error is to Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.

Type II error states that we would accept the null hypothesis given the fact that the null hypothesis was actually false. Or in other words, the probability of accepting a false hypothesis.

So, according to our question, Type II error is Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.

Rewrite the limit as

[tex]\displaystyle\lim_{x\to0}x^2\log x^2=\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}[/tex]

Then both numerator and denominator approach infinity (with different signs, but that's not important). Applying L'Hopital's rule, we get

[tex]\displaystyle\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}=\lim_{x\to0}\frac{\frac2x}{-\frac2{x^3}}=\lim_{x\to0}-x^2=\boxed{0}[/tex]

Answer:

40%

Step-by-step explanation:

1299-725= 574

574/1299 x 100 = 44.19%

The rate of discount on the dinette set = 44.2%.

Often, goods are sold at a price that is lower than their marked price. The price at which the good is sold is called the selling price and the difference between the marked price and the selling price is the discount.

Discount = Marked Price - Selling Price.

Rate of Discount = Discount/Marked Price * 100%.

In the question, we are given that Stella bought a dinette set on sale for $725. The original price was $1,299.

We are asked to calculate the rate of discount on the dinette set.

The marked price of the dinette set = $1299.

The selling price of the dinette set = $725.

∴ The discount on the dinette set = the marked price of the dinette set - the selling price of the dinette set = $1299 - $725 = $574

∴ The rate of discount on the dinette set = the discount on the dinette set/the marked price of the dinette set *100%

or, The rate of discount on the dinette set = 574/1299 * 100%

or, The rate of discount on the dinette set = 0.4418 * 100%

or, The rate of discount on the dinette set = 44.18% ≈ 44.2% (to the nearest tenth of a percent)

∴ The rate of discount on the dinette set = 44.2%.

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Answer:

True

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Two years ago, Lisa was 34 - 2 = 32 years old. If she was twice as old as her brother, he was 32 / 2 = 16 years old at that time. His age now will be 16 + 2 = 18.

Answer: [tex]\dfrac{1}{56}[/tex]

Step-by-step explanation:

Total horses = 6

Number of ways to choose top 3 finishers in order = 3! = 6

Number ways to select 3 horses out of 8 in order = [tex]^8P_3[/tex]  [By permutations]

[tex]=\dfrac{8!}{(8-3)!}=\dfrac{8!}{5!}=8\times7\times6=336[/tex]

Now, the probability that the gambler will win his bet =

[tex]\dfrac{\text{Number of ways to choose top 3 finishers }}{\text{Number ways to select 3 horses out of 8 in order}}[/tex]

[tex]=\dfrac{6}{336}\\\\=\dfrac{1}{56}[/tex]

Hence, the required probability =  [tex]\dfrac{1}{56}[/tex]

Answer:

AGE = 129 degrees

Step-by-step explanation:

Two angles whose sum is 180° are called supplementary angles. The measure of ∠AGE in the given figure is 129°.

Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

In the given figure, line segment CE is a straight line. Therefore, the sum of the angles formed on the same side of the line will be a linear pair.

Thus, the measure of the angles can be rewritten as,

∠AGC + ∠AGE = 180°

51° + ∠AGE = 180°

∠AGE = 180° - 51°

∠AGE = 129°

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Answer: B. Perpindicular Bisector.

Step-by-step explanation:

BD is a perpindicular bisector because it splits CE into 2 equal segments via a right angle.

Answer:

midsegement

Step-by-step explanation:

The correct answer is 24.5 m. You're given four different values but if you notice closely, not all the units match. Before you can add the values together, you need to get the same units. Because cm (centimeters) is the only one that's out of place, it will be easier to change it to m (meters). I think of centimeters as a century (same prefix) which equals 100. Therefore, to convert 300 cm to m, we will divide 300 by 100 to get 3. After that, add all the values together (6m+3m+3.5m+12m) to get a grand total of 24.5 m. I hope this helps!

The tape required to apply on the edge of the tape is 21.8m.

Perimeter is the sum of the length of the outer edges of a two-dimensional object.

A quadrilateral is a two-dimensional shape that is a polygon of four sides, one of the opposite sides of a quadrilateral is parallel.

Dan needs to apply tape on the edges of the stage, the tape required will be calculated by determining the perimeter of the stage.

The stage is in the shape of a quadrilateral.

The sides of the quadrilateral are as follows:

Side 1 = 6m

Side 2 = 300cm

Side 3 = 3.5m

Side 4 = 12m

300 cm will be converted into m

100 cm = 1m

300 cm = 0.3 m

The perimeter = Side 1 + Side 2 + Side 3+ Side 4

Perimeter = 6 + 0.3 +3.5 + 12

Perimeter = 21.8 m

The perimeter of the stage is 21.8m.

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Hi there! :)

Answer:

Given the information, we can write an equation in slope-intercept form

(y = mx + b) to graph the line:

Plug in the slope for 'm', the y-coordinate of the point given for 'y', and the

x-coordinate given for 'x':

-4 = -2/3(-7) + b

-4 = 14/3 + b

Solve for b:

-12/3 = 14/3 + b

-12/3 - 14/3 = b

-26/3 = b

Therefore, the equation of the line is y = -2/3x - 26/3 (Graphed below)

Some points on the line include:

(-7, -4)

(-4, -6)

(0, -26/3)

(2, -10)

(5, -12)

Answer:  without trying each calculation individually,  6750 4-digit numbers are not divisible by 4

Step-by-step explanation:  From 1000 to 9999 there are 9000 4-digit numbers 9999 - 999 = 9000.

Eliminate all the odd numbers 9000/2 = 4500

Eliminate the even numbers divisible by 2 but not by 4. 4500/2 = 2250

9000 - 2250 = 6750.

Answer: See answer in the attached file

Step-by-step explanation:

Answer:

Option (B)

Step-by-step explanation:

If two chords intersect inside a circle, measure of angle formed is one half the sum of the arcs intercepted by the vertical angles.

Therefore, 86° = [tex]\frac{1}{2}(a+c)[/tex]

a + c = 172°

Since the chords intercepting arcs a and c are of the same length, measures of the intercepted arcs by these chords will be same.

Therefore, a = c

⇒ a = c = 86°

Therefore, a = 86°

Option (B) will be the answer.

Answer:

x=60

Step-by-step explanation:

This is an equilateral triangle which means all the sides are equal.

If all the sides are equal then all the angles are equal

180/3 = 60

x=60

Answer:

x= 60°

Step-by-step explanation:

We can tell that both of these triangles are equilateral. We can tell because all of their sides have little tick marks, meaning that they are all equal, meaning that the triangle is equilateral. In an equilateral triangle, we know that through definitions all of the angles are equal to 60°. Since y is an angle inside of an equilateral triangle, it is equal to 60°

Answer:

i think it is c. i may be incorrect, i am sorry!

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I did the math

Answer:

8 hours

1 hour

8 hours

0.288675

Step-by-step explanation:

We complete the answer as follows;

mu = mean = 8 hours

sigma = standard deviation= 1 hour

Mu_x bar = mu = 8 hours

sigma_x bar = sigma/√(n) = 1/√(12) = 0.288675

Answer:

A. The variance is the positive square root of the standard deviation. The standard deviation and variance can never be negative. Squared deviations can never be negative.

Step-by-step explanation:

As we know that

The standard deviation is the square root of the variance and on the other side the variance is the square of the standard deviation

In mathematically

[tex]\sigma = \sqrt{variance}[/tex]

And,

[tex]variance = \sigma^2[/tex]

Moreover, the standard deviation and the variance could never by negative neither the squared deviation is negative. All three are always positive

Hence, the correct option is a.

Answer:

B. The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative. Squared deviations can never be negative.