3x+8-x=42

And can you please include a step-by step? I can't figure this out.

Based on the information provided, we can conduct a hypothesis test to determine if a majority of all students at Ohio University believe the academics are 'very strong'.

Let's set up the null and alternative hypotheses:

Null hypothesis (H₀): The proportion of all students who believe the academics are 'very strong' is equal to 50% or less.

Alternative hypothesis (H₁): The proportion of all students who believe the academics are 'very strong' is greater than 50%.

To test these hypotheses, we can use a one-sample proportion test. We will compare the sample proportion (55%) to the hypothesized proportion (50%) and assess if the difference is statistically significant.

Using appropriate statistical methods, such as calculating the test statistic and obtaining the p-value, we can evaluate the evidence against the null hypothesis. If the p-value is less than the chosen significance level (e.g., 0.05), we would reject the null hypothesis and conclude that a majority of all students at Ohio University believe the academics are 'very strong'. Otherwise, if the p-value is greater than the significance level, we would fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim of a majority belief.

Please note that without the actual test results or the p-value, we cannot make a definitive conclusion in this particular case.

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We can conclude that △XYB is congruent to △ZYA (△XYB ≅ △ZYA) under the ASA congruency condition.

If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent.

SSS, which stands for "side, side, side," denotes that there are two triangles with identical angles on all three sides.

"Side, Angle, Side" stands for two triangles whose two sides and one included angle are known to be equal.

So, we know that:

To prove: △XYB ≅ △ZYA

∠X = ∠Z (Given)

XY = ZY (Given)

∠Y = ∠Y (Common angle)

Hence, △XYB ≅ △ZYA is under ASA condition.

Therefore, we can conclude that △XYB is congruent to △ZYA (△XYB ≅ △ZYA) under the ASA congruency condition.

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Correct question:

What additional information would be necessary to prove that the two triangles, △XBY and △ZAY, are congruent? What congruency theorem would be applied?

Given: ∠X ≅ ∠Z and (XY) ≅ (ZY)

If the lamp is 3.6 m above the ground, the length of her shadow is 1.2 m.

In algebra proportionality is equality between two ratios. In the mathematical expression a/b = c/d, a and b are in the same proportion as c and d.

Height of the girl = 0.9 m.

Height of the lamp = 3.6 m.

Distance between the lamp and the girl = 4.8 m.

Let the length of her shadow = x m.

From proportionality relation:

3.6 : 4.8 = 0.9 : x

3.6/4.8 = 0.9/x

3.6x = 4.8 × 0.9

x  = (4.8 × 0.9) ÷ 3.6

x = 1.2

Hence, the length of her shadow is 1.2 m.

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Answer:

0.100100010000...

Step-by-step explanation:

becoz in irrational numbers decimal goes on forever

Answer: It sounds as if you worded it correctly the first time, though for a math assignment, I probably wouldn't use the term "doubled" (though it is technically correct)

Step-by-step explanation:

G = 2B is "The total number of girls is two times the number of boys"

B = 2G is "The total number of boys is two times the number of girls"

Answer:

Step-by-step explanation:

Hello!

The answer is Option A.

Run-on sentences are two short sentences put together without being properly connected.

"They were expensive combs" and "her heart had simply craves and yearned over them" are two short sentences that are put together.

Hope it helps!

If you have any questions, feel free to ask me!

~A gloomy gal

\(MagicalNature\)

A23425

Step-by-step explanation:

The equation in the form \(x^{2}\) + bx = c is \(x^{2}\) - 2x = 15.

By adding to both sides the term needed to complete the square is 1.

Factors of the perfect square trinomial are 5 and - 3.

As per the given data the given equation is:

\(x^{2}\) - 2x - 15 = 0

1. Rewrite the equation in the form \(x^{2}\) + bx = c

Since a = 1 keep the “x-terms” (both the squared and linear terms) on the left side but move the constant to the right side.

Add 15 on both sides of the equation.

\(x^{2}\) - 2x - 15 + 15 = 0 + 15

\(x^{2}\) - 2x = 15

2. Add to both sides the term needed to complete the square.

Divide by 2, followed by squaring (raising to the 2 nd power).

\(& x^2-2 x=15 \\\)

\(& \left(\frac{-2}{2}\right)^2=1\)

The output here, which is +1, will be added to both sides of the quadratic equation.

\(x^{2}\) - 2x + 1 = 15 + 1

\(x^{2}\) - 2x + 1 = 16

\((x-1)^2=16\) (Perfect square trinomial express into square of a binomial)

3. Factor the perfect square trinomial.

\(\sqrt{(x-1)^2} & =\pm \sqrt{16} \\\)

x - 1 = ± 4

x - 1 + 1 = ± 4 + 1

x = ± 4 + 1

x = 4 + 1           x = -4 + 1

x = 5                x = - 3

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Answer:

10

Step-by-step explanation:

2kg and 500g is 2.5kg. 25kg÷2.5 is 10

Answer:
A part to part ratio is the porportion if the diff parts in relation to each other

Step-by-step explanation:

Based on the provided voltage readings, the polarity of the single-phase transformer can be identified as follows: the dot notation represents the primary winding, while the numerical labels indicate the corresponding terminals.

The primary and secondary windings are denoted by L1 and L2, respectively. The polarities can be determined by observing the voltage readings across various terminal combinations.

To identify the polarity of a single-phase transformer, you can analyze the voltage readings obtained from different terminal connections. In this case, let's consider the given readings.

When measuring the voltage between L1 and L2, we obtain a reading of 121 volts. This indicates the voltage across the primary and secondary windings in the same direction, suggesting a non-reversed polarity.

Next, measuring the voltage between terminals 1 and 4 while connecting terminals 2 and 3 results in a reading of 26.47 volts. This implies that terminals 1 and 4 have the same polarity, while terminals 2 and 3 have opposite polarities.

Similarly, when connecting terminals 2 and 4 and measuring the voltage between terminals 1 and 3, a reading of 7.32 volts is obtained. This indicates that terminals 1 and 3 have the same polarity, while terminals 2 and 4 have opposite polarities.

For the combination of terminals 6 and 7, a voltage reading of 25.78 volts is measured between terminals 5 and 8. This suggests that terminals 5 and 8 have the same polarity, while terminals 6 and 7 have opposite polarities.

Lastly, when connecting terminals 5 and 7 and measuring the voltage between terminals 6 and 8, a reading of 5.42 volts is obtained. This indicates that terminals 6 and 8 have the same polarity, while terminals 5 and 7 have opposite polarities.

By considering the polarity relationships observed in these readings, we can conclude that the primary and secondary windings of the single-phase transformer have the same polarity. The dot notation indicates the primary winding, and the numerical labels represent the terminals.

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The maturity value of the investment would be $8,858.80.

To calculate the maturity value, we need to calculate the compound interest for each period separately and then add them together.

For the first 18 months, the interest is compounded semi-annually at a rate of 5%. Since there are two compounding periods per year, we divide the annual interest rate by 2 and calculate the interest for each period. The formula for compound interest is A = P(1 + r/n)^(nt), where A is the maturity value, P is the principal amount, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years. Plugging in the values, we get A = 8000(1 + 0.05/2)^(2*1.5) = $8,660.81.

For the next 5 months, the interest is compounded monthly at a rate of 10%. We use the same formula but adjust the values for the new interest rate and compounding frequency. Plugging in the values, we get A = 8000(1 + 0.10/12)^(12*5/12) = $8,858.80.

Therefore, the maturity value of the certificate after the specified period would be $8,858.80.

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Answer:

\(\huge\underline\mathtt\colorbox{cyan}{Alt-interior Angles}\)

Step-by-step explanation:

Angles 4 and 3 are a pair of alternate-interior angles which are equal in measure.

Answer:

26d+70,000=m

Step-by-step explanation:

you're using a y=mx+b format

so the slope is 26 because she drives 26 miles every day (d), and she already has 70,000 miles on her car

The limits from both sides are different, the limit does not exist. Therefore, the answer is DNE.

To evaluate the given limit:

lim t→7 (t² - 4t - 21) / (t - 7)

We first notice that the denominator becomes zero as t approaches 7, which means the function is not defined at t=7. We must check whether there is a limit from both sides of 7.

Let's approach the limit from the left side of 7. We substitute t=7 - h, where h is a positive number approaching zero.

lim h→0- [(7 - h)² - 4(7 - h) - 21] / [(7 - h) - 7]

= lim h→0- [49 - 14h + h² - 28 + 4h - 21] / (-h)

= lim h→0- (-h² - 10h) / (-h)

= lim h→0- (h² + 10h) / h

= lim h→0- (h + 10) = -10

Now, let's approach the limit from the right side of 7. We substitute t=7 + k, where k is a positive number approaching zero.

lim k→0+ [(7 + k)² - 4(7 + k) - 21] / [(7 + k) - 7]

= lim k→0+ [49 + 14k + k² - 28 - 4k - 21] / k

= lim k→0+ (k² + 10k) / k

= lim k→0+ (k + 10) = 10

Since the limits from both sides are different, the limit does not exist. Therefore, the answer is DNE.

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Answer:

3_5/6 hours

Step-by-step explanation:

2_ 1/3 = 2_ 4/12

1_3/4 = 1_6/12

2_4/12 + 1_6/12 = 3_10/12

3_10/12 = 3_5/6

Answer:

how are you supposed to solve that??? I'm confused ://

Part A

Given info:

Because n > 30 is not true, and we don't know the population standard deviation (sigma), this means we must use a T distribution.

The degrees of freedom here are n-1 = 23-1 = 22.

At 90% confidence and the degrees of freedom mentioned, the t critical value is roughly t = 1.717

Use a T distribution table or calculator to determine this. If you don't have a calculator for the task, then you can search out "inverse T calculator" and there are tons of free options to pick from.

The margin of error E is

E = t*s/sqrt(n)

E = 1.717*1.12/sqrt(23)

E = 0.400982

This is approximate and accurate to 6 decimal places.

The confidence interval is going to be xbar plus or minus that E value

L = lower bound = xbar - E = 4.90 - 0.400982 = 4.499018 = 4.50

U = upper bound = xbar + E = 4.90 + 0.400982 = 5.300982 = 5.30

The confidence interval in the format of (L, U) is (4.50, 5.30)

You could also express it as the format L < mu < U and it would be 4.50 < mu < 5.30; however, I'll stick to the first method.

=====================================================

Part B

Since we know sigma = 2.6 is the population standard deviation, we can use a Z distribution now.

At 90% confidence, the z critical value is roughly 1.645; use a table or calculator to determine this.

\(n = \left(\frac{z*\sigma}{E}\right)^2\\\\n \approx \left(\frac{1.645*2.6}{0.03}\right)^2\\\\n \approx 20325.254444 \\\\\)

Round this up to the nearest integer to get 20326. For min sample size problems, always round up.

Answer:

The angle created between the ladder and tree is \(15.5^{0}\).

Step-by-step explanation:

The required sketch is shown in the attachment to this answer.

Applying the appropriate trigonometric function to the question, we have;

Tan θ = \(\frac{Opposite side}{Adjacent side}\)

         = \(\frac{5}{18}\)

         = 0.2777777777

⇒ θ = \(Tan^{-1}\) 0.2777777777

      = 15.5241

      = \(15.5^{0}\)

Therefore, the angle created between the ladder and tree is \(15.5^{0}\).

Answer:3

Step-by-step explanation:

9/16 - 3/4

First make these fractions have the same denominator which in this case will be 16 so the equation will be 9/16- 12/16 and 12-9= 3 so therefore Scott ate 3 more pizzas than Owen

The required manager has 12 fifty-dollar bills as of the given condition.

Let's denote the number of twenty-dollar bills as "x" and the number of fifty-dollar bills as "y".

We know that the convention manager has a total of 48 bills, so:
x + y = 48

We also know that the total amount of money she has is $1320, which can be expressed as:
20x + 50y = 1320

To solve for "y", we can rearrange the first equation to get:
y = 48 - x

Then substitute this expression for "y" in the second equation:

20x + 50(48 - x) = 1320

Expanding the expression and simplifying:
20x + 2400 - 50x = 1320
-30x = -1080
x = 36

So the manager has 36 twenty-dollar bills. To find the number of fifty-dollar bills, we can use the first equation:

x + y = 48

36 + y = 48

y = 12

Therefore, the manager has 12 fifty-dollar bills.

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Answer: If there is 50 in each box, yes.

Step-by-step explanation:

The exact value of (sin 5π/8 + cos 5π/8)² is 2

To evaluate the exact value of (sin 5π/8 + cos 5π/8)², we can use the trigonometric identity (sin θ + cos θ)² = 1 + 2sin θ cos θ.

In this case, we have θ = 5π/8. So, applying the identity, we get:

(sin 5π/8 + cos 5π/8)² = 1 + 2(sin 5π/8)(cos 5π/8).

Now, we need to determine the values of sin 5π/8 and cos 5π/8.

Using the half-angle formula, sin(θ/2), we can express sin 5π/8 as:

sin 5π/8 = √[(1 - cos (5π/4))/2].

Similarly, using the half-angle formula, cos(θ/2), we can express cos 5π/8 as:

cos 5π/8 = √[(1 + cos (5π/4))/2].

Now, substituting these values into the expression, we have:

(sin 5π/8 + cos 5π/8)² = 1 + 2(√[(1 - cos (5π/4))/2])(√[(1 + cos (5π/4))/2]).

Simplifying further:

(sin 5π/8 + cos 5π/8)² = 1 + 2√[(1 - cos (5π/4))(1 + cos (5π/4))/4].

Now, we need to evaluate the expression inside the square root. Using the angle addition formula for cosine, cos (5π/4) = cos (π/4 + π) = cos π/4 (-1) = -√2/2.

Substituting this value, we get:

(sin 5π/8 + cos 5π/8)² = 1 + 2√[(1 + √2/2)(1 - √2/2)/4].

Simplifying the expression inside the square root:

(sin 5π/8 + cos 5π/8)² = 1 + 2√[(1 - 2/4)/4]

                                = 1 + 2√[1/4]

                                = 1 + 2/2

                                = 1 + 1

                                = 2.

Therefore, the exact value of (sin 5π/8 + cos 5π/8)² is 2.

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Total number of students that likes both dog and Cat = 194 students.

Total number of students = 335 students

Therefore,

percentage = 58%

Answer:

y= 128(1-.5)^t

Step-by-step explanation:

Answer:

See Explanation

Step-by-step explanation:

Given

\(Pea = \$ 3\frac{3}{4}\)

\(Corn = \$ 1\frac{1}{2}\)

Required: Determine the total sales

The amount of peas and corns sold are not given. So, I will make some assumptions

If 1 square foot of pea is sold at \(\$ 3\frac{3}{4}\), then p square feet will be sold at: \(\$ 3\frac{3}{4}p\)

Similarly:

If 1 square foot of corn is sold at \(\$ 1\frac{1}{2}\), then c square feet will be sold at: \(\$ 1\frac{1}{2}c\)

So, the total is:

\(Total = 3\frac{3}{4}p + 1\frac{1}{2}c\)

\(Total = \frac{15}{4}p + \frac{3}{2}c\)

Assumptions

\(p = 8\)

\(c =6\)

The equation becomes:

\(Total = \frac{15}{4}*8 + \frac{3}{2}*6\)

\(Total = 15 * 2 + 3 * 3\)

\(Total = 30+ 9\)

\(Total = \$39\)

Answer: can someone help i really need it <( _ _ )>

Step-by-step explanation:

help btw i think it is 3 as a hole and 3\8 as a fraction i need to learn about fractions more

Answer:

16 circumference ohh area and circumference is same man\women

The product of the factors of \(65x^2 + 212x - 313\) is equal to the original expression. Lauren may have recognized the expression as a difference of squares and factored it accordingly.

We can first simplify the expression \(65x^2 + 212x - 313\) by factoring it:

\(65x^2 + 212x - 313 = (13x - 1)(5x + 313)\)

(13x - 1)(5x + 313) = \(65x^2 + 212x - 313\)

Therefore, the product of the factors is equal to the original expression.

To see this, we can rewrite the expression as:

\(65x^2 - 313 - 212x = (5x)^2 - (2\cdot 5x \cdot 7) + 7^2 - 7^2 - 212x\)

= \((5x - 7)^2 - 7^2 - 212x\)

= \((5x - 7)^2 - 212x - 49\)

= \((5x - 7)^2 - 1^2\cdot 49 - 212x\)

= (5x - 7 - 7)(5x - 7 + 7) - 49 = (5x - 14)(5x) - 49

= 5x(5x - 14) - 49

= 5x(5(x - 2) - 9)

= 5x(5x - 29)

Therefore, the factors of the expression are (5x - 7) and (5x - 29).

Lauren may have recognized the expression as a difference of squares by noticing that the coefficient of the x term (212) is twice the product of the square roots of the first and last terms (sqrt(65) and sqrt(313)), which is a common characteristic of a difference of squares.

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For measurable subset A ⊆ R, a ∈ (0,1), p, q, r ≥ 1 (p, q ≥ r), the inequality \((1-a)^r\) ||f||r ≤ ||f||p-q * r/(1-a) holds for any measurable function f on N.

To prove the inequality 1-a ≤ ||f||p ||f||q, we'll first show that p and q are conjugate exponents, and then use Hölder's inequality.

Showing p and q are conjugate exponents:

Given p, q, and r ≥ 1, where p, q ≥ r, we need to show that 1/p + 1/q = 1/r.

Since 1/p + 1/q = (p+q)/(pq), and 1/r = 1/(pq), we want to prove (p+q)/(pq) = 1/(pq).

Multiplying both sides by pq, we get p+q = 1, which is true since a ∈ (0, 1).

Applying Hölder's inequality:

For any measurable function f on N, we can use Hölder's inequality with exponents p, q, and r (where p, q ≥ r) as follows:

||f||p ||f||q ≥ ||f||r

Using the given inequality 1-a ≤ ||f||p ||f||q, we have

1-a ≤ ||f||p ||f||q

Dividing both sides by ||f||r, we get:

(1-a) ||f||r ≤ ||f||p ||f||q / ||f||r

Simplifying the right side, we have:

(1-a) ||f||r ≤ ||f||p-q

Finally, since r ≥ 1, we can raise both sides to the power of r/(1-a) to obtain

[(1-a) ||f||r\(]^{r/(1-a)}\) ≤ [||f||p-q\(]^{r/(1-a)}\)

This simplifies to

\((1-a)^{r/(1-a)}\) ||f||r ≤ ||f||p-q * r/(1-a)

Notice that \((1-a)^{r/(1-a)}\) = \((1-a)^r\), which gives

\((1-a)^r\) ||f||r ≤ ||f||p-q * r/(1-a)

This completes the proof.

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27 Hope this helps :T

Answer:

27 Ans ......

Step-by-step explanation:

Given:

=√3x9x27

Solution:

=√3x9x27

=√729

=27 Ans ...... .