Simplify:
2 +5.6
12 + 22

Answer:

6.104

Step-by-step explanation:

Given that,

Mean, {eq}\mu = 6.8 {/eq}

Standard deviation, {eq}\sigma = 0.37 {/eq}

{eq}P(X < x) = 0.03\\ P(\dfrac{X - \mu}{\sigma} < \dfrac{x - \mu}{\sigma}) = 0.03\\ P(Z < \dfrac{x - 6.8}{0.37}) = 0.03\\ P(Z < z) = 0.03 {/eq}

Excel function for the value of z:

=NORMSINV(0.03)

{eq}z = -1.881\\ \dfrac{x - 6.8}{0.37} = -1.881\\ x = 6.8-1.881\times 0.37\\ \color{blue}{x = 6.104 \ minutes} {/eq}

To be sponsored by the running shoe company as one of the fastest 3% of runners, one would need to run faster than the upper 3rd percentile of runners. This can be calculated using the z-score formula which is given as; z = (x - μ) / σ where x is the value we want to find the percentile of, μ is the mean and σ is the standard deviation.

The z-score formula can be rearranged to solve for x which is the running time needed to be sponsored by the company as follows;x = z * σ + μWe want to find the upper 3rd percentile, which corresponds to a z-score of 1.88 (from z-tables or calculator).

Therefore;1.88 = (x - 7.2) / 0.56. Rearranging to solve for x;x = 1.88 * 0.56 + 7.2x = 8.1888 (rounded to 4 decimal places)Therefore, one would need to run faster than 8.1888 minutes to be sponsored by the running shoe company as one of the fastest 3% of runners.

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Answer:

Howard works 7x+7 hours in a week

Step-by-step explanation:

Equations

Ron and Howard work at Amazon.

Ron works x hours each week for 7 days. This means he works 7x hours a week.

Howard works one more hour per day than Ron, thus he works x+1 hours per day. This means he works 7(x+1)=7x+7 hours a week.

Howard works 7x+7 hours in a week

There are 360 black counters and 306 white counter in 20:17 ratio.

Let's denote the number of black counters by B and the number of white counters by W. We know that the ratio of black to white counters is 20:17, which means that:

B/W = 20/17

We also know that there are 54 more black counters than white counters, which means that:

B = W + 54

We can use substitution to solve for B. Substituting the second equation into the first equation, we get:

(W + 54)/W = 20/17

Cross-multiplying, we get:

17(W + 54) = 20W

Expanding the left side, we get:

17W + 918 = 20W

Subtracting 17W from both sides, we get:

918 = 3W

Dividing both sides by 3, we get:

W = 306

Now we can use the second equation to find B:

B = W + 54 = 306 + 54 = 360

Therefore, there are 360 black counters in the bag.

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We want to find "3/6" of 30.

First of all, let's reduce the fraction (3/6th).

Dividing top and bottom by 3, we have:

3/6

3/3 divided by 6/3

1 divided by 2

This is half.

So, we need half of 30. Which basically means:

Thus,

3/6 of 30

is

Answer:

- It lies inside an acute triangle

- It lies on a right triangle.

- It lies outside an obtuse triangle.

Answer:

so what we have to do first is multiply 9*10

which is 90 now we divide by two to get 45

now we multiply 45 by 20 to get

900

Hope This Helps!!!

Step-by-step explanation:

13) 4x-22+x+11+10x-4 =180

15x=195

x=13

<P=(10(13)-4)=126

<Q=(4(13)-22)=30

<R=13+11=24

If Station 1 (at 74, 41) is 44 km away and Station 2( at 0,43 ) is 38 km away. The required approximate location of the GPS receiver is (42, 10).

The location of the GPS receiver can be determined with the help of trilateration. Trilateration is a process of determining absolute or relative locations of points by measurement of distances, using the geometry of circles, spheres, or triangles. If three stations (or more) are in known locations, with a known distance from the point of interest, we can determine the position of the GPS receiver with the help of trilateration.

It can be determined by the following method:

1: Plot the given stations on a coordinate plane. Stations are:

Station 1: (74, 41)

Station 2: (0, 43)

2: Calculate the distance of the GPS receiver from each station using the distance formula.

Distance Formula: The distance formula is used to find the distance between two points in the coordinate plane. The distance between points (x1,y1) and (x2,y2) is given by

d = √[(x2 - x1)² + (y2 - y1)²]

Station 1: Distance from station 1 = 44 kmSo, d1 = 44 km

Station 2: Distance from station 2 = 38 kmSo, d2 = 38 km

3: Plot the given distances as the circle on the coordinate plane.

Circle 1: Centred at (74, 41) with a radius of 44 km.

Circle 2: Centred at (0, 43) with a radius of 38 km.

4: The intersection of two circles. Circle 1 and Circle 2 intersect at point P (approx) (42, 10). So, the approximate location of the GPS receiver is (42, 10).

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The n 1/2 of the se 1/4 of the sw 1/4 and the ne 1/4 of the sw 1/4 of Section 19 contains 40 acres.

The method used for land surveying is called the government rectangular survey system.

This system is commonly known as the Public Land Survey System (PLSS) of the United States. It is based on a grid network. The grid is formed with meridians and baselines.

The meridians are the imaginary lines running north to south, and the baselines are the imaginary lines running east to west. The meridians and baselines are named as ranges and townships, respectively.

Each range is 6 miles wide and numbered consecutively, beginning with the one on the far west side of the state. The townships are numbered from 1 to 36, in sequence, beginning at the southeast corner of the state. The government rectangular survey system divides the land into smaller units as follows:

Each township is further divided into 36 sections, each section is one square mile, or 640 acres.

Each section is further divided into halves, or 320 acres, and each half is divided into quarters, or 160 acres, and each quarter is divided into quarters again, or 40 acres.

Finally, each 40-acre parcel is divided into quarters, or 10 acres.

Therefore, the n 1/2 of the se 1/4 of the sw 1/4 and the ne 1/4 of the sw 1/4 of section 19 contains 40 acres.

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Hello,

U (n +1) = Un + 6

Un = Uo + nr

U9 = 7 + 9 × 6 = 7 + 54 = 61

Answer:

nth term = 6n + 1.

Step-by-step explanation:

The first term a1 = 7 and the common difference d =  6.

nth term = a + d(n - 1)

= 7  + 6(n - 1)

= 6n + 1.

The time categories are divided into "<1 hour," "1-2 hours," "2-3 hours," and ">3 hours."  

What does the frequency distribution in the table reveal about the homework habits of the two samples of high school students?

The frequency distribution in the table provides insights into the distribution of homework habits among the two samples of high school students. By examining the frequency counts in each time category, we can determine the proportion of students spending different amounts of time on homework each night. This information helps identify patterns and differences in homework habits between the two samples, allowing for a comparison of their study behaviors.

Here is an example of a 4-column table with 2 rows representing the results of a random survey asking two samples of 100 high school students about the amount of time they spend on homework each night:

Sample 1:

  Sample 1                                                     Number of Students

    Time                                                                   Frequency

   <1 hour                                                                     20

  1-2 hours                                                                    40

 2-3 hours                                                                     30

    >3 hours                                                                   10

Sample 2:

 Sample 2                                                        Number of Students

Time                                                                      Frequency

<1 hour                                                                        30

1-2 hours                                                                    35

2-3 hours                                                                   20

>3 hours                                                                      15

In this table, each sample represents a different group of 100 high school students, and the frequency of students spending a particular amount of time on homework each night is recorded. The time categories are divided into "<1 hour," "1-2 hours," "2-3 hours," and ">3 hours." The table provides an overview of the distribution of homework time among the two samples of high school students.

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Answer:

si=part

=2500×0.045×2

=225...

the answer is C

Answer:

the answer is 83°

Step-by-step explanation:

by the sum of iner and outer angle=180°

180-126= 54°

x=180-43+54

x=180-97

x=83°

The measure of angle x is 43°.

What is Triangle?

A triangle is a three sided polygon , which has three vertices.

Given that;

In triangle, The value of interior angles are 43° and x°.

And, An exterior angle is 126°.

Since, The sum of two interior angles is equal to the exterior angle of same triangle.

Hence, We can formulate;

43° + x = 126°

Subtract 43° both side;

43° + x - 43° = 126° - 43°

x = 83°

Thus, The measure of angle x is 43°.

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The simplified form of the expression 1/5 divied by 2 as a fraction is 1/10.

Given the expression in the question;

1/5 divied by 2

1/5 ÷ 2

To simplify, multiply 1/2 by the reciprocal of 2

1/5 ÷ 2

1/5 × 1/2

Simplify

( 1 × 1 ) / ( 5 × 2 )

( 1 ) / ( 5 × 2 )

Multiply 5 and 2

( 1 ) / ( 10 )

1/10

Therefore, the simplified form is 1/10.

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The correct research method for the study mentioned in the question is a Field survey.

Field survey can be defined as a research method used to collect data from a target population. In this study, researchers used a survey questionnaire to gather data from participants. The research aimed to test the theory that the exposure to multiple versions of fake news on various social media platforms made people believe the news.

The researchers surveyed 1,455 participants with an average age of 27, and 42% were male. The participants were exposed to 24 false news stories, and one group was exposed to multiple versions of fake news, while the other group was only exposed to each news story once.

The findings suggested that the more familiar the news was, the more accurate and believable it was. This familiarity effect lasted for up to a month. Hence, the research method used in this study was a field survey.

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Answer:

360 degrees

Step-by-step explanation:

Answer:

Aisha wrapped 17 presents.

Step-by-step explanation:

If each present weighs 1/3 kilograms (the "kilograms" doesn't matter, just the weight of each present and the combined weight), and 3 presents fit in one kilogram, then 15 can fit in 5 kilograms, and 2 more can fit in the remaining two thirds.

Answer:

The answer is 17 presents.

Step-by-step explanation:

Each present weighs 1/3 kg. so you turn 5 2/3 into an improper fraction, 17/3. And then now you do 17/3 divided by 1/3, which gives you 17.

The vertex of the parabola represented by the equation -3x² - 12x - 23 = y - 8 is (-2, -63).

To find the vertex of the parabola using completing the square, we can rewrite the equation in the form:

\(y = a(x - h)^2 + k\)

Where (h, k) represents the coordinates of the vertex.

Let's complete the square for the given equation:

\(-3x^2 - 12x - 23 = y - 8\)

First, we'll move the constant term to the right side of the equation:

\(-3x^2 - 12x = y - 8 + 23\\-3x^2 - 12x = y + 15\)

Next, we'll factor out the coefficient of \(x^2 (-3)\) from the first two terms:

\(-3(x^2 + 4x) = y + 15\)

To complete the square, we need to take half of the coefficient of x (4), square it (16), and add it inside the parentheses. However, since we added it inside the parentheses, we need to subtract 16 * (-3) from the right side to maintain the equality:

\(-3(x^2 + 4x + 4) = y + 15 - 16 * (-3)\\-3(x + 2)^2 = y + 15 + 48\\-3(x + 2)^2 = y + 63\\\)

Now, we can rewrite the equation in the vertex form:

\(y = -3(x + 2)^2 - 63\)

Comparing this with the vertex form equation: \(y = a(x - h)^2 + k\), we can see that the vertex is at the point (-2, -63).

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The vertex of the parabola is (-2, -19).

To find the vertex of the parabola given by the equation \(-3x^2 - 12x - 23 = y - 8\), we can complete the square. The general form of a quadratic equation is \(y = ax^2 + bx + c,\) where (h, k) represents the vertex of the parabola.

First, let's rewrite the equation in the standard form:

\(-3x^2 - 12x + 15 = y.\)

Now, we can complete the square. To do this, we need to take half of the coefficient of x (-12) and square it: \((-12/2)^2 = 36.\)

Add 36 to both sides of the equation: \(-3x^2 - 12x + 15 + 36 = y + 36.\)

Simplify: \(-3x^2 - 12x + 51 = y + 36.\)

Now, we can rewrite the equation in vertex form by factoring the left side: \(-3(x^2 + 4x - 17) = y + 36.\)

Next, we complete the square within the parentheses:

\((x + 2)^2 = -3(y + 19).\)

Now, the equation is in the form \((x - h)^2 = 4p(y - k)\), where (h, k) represents the vertex. In this case, the vertex is (-2, -19).

Overall, the process involves rewriting the equation in standard form, completing the square, and then rearranging the equation to match the vertex form. This allows us to identify the vertex of the parabola.

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Answer: $26.24

Step-by-step explanation:

Same method

The average (mean) of all 5-digit numbers that can be formed by using each of the digits 1, 3, 5, 7, and 8 exactly once is 53332.8

Since the numbers 1, 3, 5, 7, and 9 are all 2 apart from one another, we may start by finding the mean for those numbers. These digits may be used to solve any number, and the mean of those numbers is 55555. These digits may be used to create 5! = 120 different numbers. These numbers add up to 55555(120) = 6666600. Now we can calculate the overall benefit of changing the 8 to a 9. Starting from the point where the 8 was in the ones digit, we may calculate the gain. Since 1 was obtained from each of the 4! = 24 numbers with an 8 in the ones digit, the result is 24.

Then, we repeat this with the tens, hundreds, thousands, and ten thousand place, leading to a total of 24+240+2400+24000+240000=266664 as the total amount that was gained. Subtract this amount from the sum of the digits using the 9 instead of the 8 to get 6666600-266664=6399936. Finally, we divide this by 120 to get the average. 6399936/120

= 53332.8

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\(\implies {\blue {\boxed {\boxed {\purple {\sf { \: A. \:1 \frac{1}{2} }}}}}}\)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

\( - 2 \frac{1}{4} \div ( - 1 \frac{1}{2} )\)

➼ \( \: \frac{ - 9}{4} \div( \frac{ - 3}{2} )\)

➼ \( \: \frac{ - 9}{4} \times \frac{ - 2}{3} \)

➼ \( \: \frac{ - 9 \times - 2}{4 \times 3} \)

➼ \( \: \frac{18}{12} \)

➼ \( \: \frac{3}{2} \)

➼ \( \: 1 \frac{1}{2} \)

\(\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}\)

Answer: \(\sqrt{3}\) x 8 = 13.8564064606

Step-by-step explanation: The main diagonal of any cube can be found by multiplying the length of one side by the square root of 3 (\(\sqrt{3}\)). Therefore, square root 3 (\(\sqrt{3}\)) is multiplied by the length (8 in our case) of either 6 faces of the cube.

Hope it helped!

Answer:

13.8564064606

Answer:

Each person will get 5 slices.

Step-by-step explanation:

To get 7 slices shared evenly, each person will have 5.

Why 5?

36/7 = 5.143

There cannot be 5.143 of a slice.

7 x 5 = 35 with one left over slice.