factorise x square - 7 x minus 42​

Answer:

The product 12 × 15 in friendlier numbers is (10 + 2) × (10 + 5) = 180

Step-by-step explanation:

The parameter given are;

To 12 × 15 by changing the numbers into friendlier numbers

The product in 12 × 15 written with friendlier numbers (or in a simplified format can be given as follows;

12 × 15 = (10 + 2) × (10 + 5)

Which gives;

(10 + 2) × (10 + 5) = 10² + 10 × 5 + 2 × 10 + 2 × 5

From which we have;

10² + 10 × 5 + 2 × 10 + 2 × 5 = 100 + 50 + 20 + 10 = 180

Therefore;

12 × 15 = 180.

Answer:

1 minute to sail 17/306 = 1/18th of a nautical mile

234 minutes to sail 1/18 x 234 = 13 nautical miles.

Hope this helps :-)

Step-by-step explanation:

Answer:

15 nautical miles

Step-by-step explanation:

Set up a proportion: 340/17=300/x simplify the first one 20/1=300/x 20x=300 x=15 so 15 nautical miles

Please mark brainliest if correct Hope this helps :D

Answer:

1) 7 times a number

2) m + 3

3) n/2

Step-by-step explanation:

(a)  95% CI for μ when n=25 and x will be (51.68, 55.52) watts .

We use the formula for a confidence interval for the mean with known standard deviation:

CI = (x - z*σ/√n, x+ z*σ/√n)

where x is the sample mean, σ is the population standard deviation, n is the sample size, and z is the z-score corresponding to the desired confidence level (95% in this case).

Since the standard deviation is unknown, we use the sample standard deviation s as an estimate for σ.

Plugging in the values, we have:

CI = (53.6 - 1.96*(s/√25), 53.6 + 1.96*(s/√25))

  = (51.68, 55.52) watts

(b) 95% CI for μ when n=100 and x will be (52.42, 54.78) watts.

Using the same formula as in part (a), we have:

CI = (53.6 - 1.96*(s/√100), 53.6 + 1.96*(s/√100))

  = (52.42, 54.78) watts

(c) 99%CI for μ when n=100 and x will be (51.96, 55.24) watts

Using the same formula as in part (a) with a z-score of 2.58 (corresponding to a 99% confidence level), we have:

CI = (53.6 - 2.58*(s/√100), 53.6 + 2.58*(s/√100))

  = (51.96, 55.24) watts

(d) 82% CI for μ when n=100 and x will be (52.95, 54.25) watts

Using the same formula as in part (a) with a z-score of 1.305 (found using a standard normal table or calculator), we have:

CI = (53.6 - 1.305*(s/√100), 53.6 + 1.305*(s/√100))

  = (52.95, 54.25) watts

(e) The value of n will be 267.

We use the formula for the width of a confidence interval:

width = 2*z*(s/√n)

where z is the z-score corresponding to the desired confidence level (99% in this case) and s is the sample standard deviation.

Solving for n, we have:

n = (2*z*s/width)^2

Plugging in the values, we get:

n = (2*2.58*s/1.0)^2

 = 266.49

Rounding up to the nearest whole number, we get n = 267.

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For the given question value of x will be 20

Congruent triangle:

                                If two triangle are congruent then all the corresponding sides and corresponding angles ill be equal. Symbol for congruent is ≅.Congruent triangles are also known as identical triangle.

For example,

                    if ΔMNP and ΔSQR are congruent,

that is,

                    if  ΔMNP ≅ ΔSQR

then,

                ∠M = ∠S

                ∠N = ∠Q

                ∠P = ∠R

and ,

          MN = SQ  , NP = QR , MP = SR

According to question,

       ∠S = (3x+5)°    

       ∠N = (4x-6)°    

        ∠R = (2x+1)°    

        ∠Q = (94-x)°

As,

           ΔMNP ≅ ΔSQR

so,

          ∠N = ∠Q

     (4x-6)° = (94-x)°

      4x + x = 94 + 6

        5x = 100

         x = 100/5

         x = 20

Hence, for the given congruent triangle ΔMNP and ΔSQR value of x will be 20.

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The terms minimum and infimum are both related to the concept of lower bounds in mathematics. A minimum is the smallest value in a set of numbers, whereas an infimum is the greatest lower bound of a set.

A minimum is a value that is less than or equal to all other values in the set, while an infimum is a value that is less than or equal to all other values in the set, but not necessarily the smallest value.

For example, if we consider the set {2, 4, 6}, the minimum is 2 and the infimum is also 2. However, if we consider the set {2, 4, 6, 8}, the minimum is 2 and the infimum is 4. In the latter set, 4 is the greatest lower bound, meaning that all other values in the set are greater than or equal to 4.

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Answer:

0.08(50h)

Step-by-step explanation:

0.08(50h)+50h=

8/100(50h)+50h=

0.08(50h)+50h

It's 0.08 of 50h, so

0.08(50h)

Answer:

3 dollars

Step-by-step explanation:

Answer:

$3

Step-by-step explanation:

If the unit price is 1.5 , you multiply it by 2 to get the price of 2 pounds

1.5*2=$3

The book is opened to pages 11 and 12.

How to get the product of the page

x * (x + 1) = 132

Expanding the equation, we get:

x² + x = 132

To solve for x, we need to rewrite the equation as a quadratic equation:

x²+ x - 132 = 0

Now, we can factor the quadratic equation:

(x - 11)(x + 12) = 0

This equation has two solutions for x:

x = 11

x = -12

Since page numbers cannot be negative, we discard the second solution. Thus, the left-hand page number is 11, and the right-hand page number is 11 + 1 = 12.

So, the book is opened to pages 11 and 12.

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Option a,The correct null hypothesis for an independent-measures t test is option a, which states M1 - M2 = 0.

An independent-measures t test is a statistical test used to compare the means of two independent groups. In this test, the null hypothesis represents the assumption that there is no significant difference between the means of the two groups. The null hypothesis is usually expressed in terms of the difference between the means of the two groups, denoted by M1 and M2.

In summary, the correct null hypothesis for an independent-measures t test is option a, which states M1 - M2 = 0. This null hypothesis assumes that there is no significant difference between the means of the two groups and any observed difference is due to chance. Option b assumes a significant difference between the means, while options c and d use population means instead of sample means. It is important to correctly specify the null hypothesis in a statistical test to ensure that the conclusions drawn from the analysis are valid.

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we have

8.08x5.07=40.9656

therefore

the product has 4 digits after the decimal point

The pollster should survey 2627 voters in order to be 96 percent confident that the true proportion of U.S. voters opposing capital punishment is estimated to within 0.02.

To determine the sample size needed for estimating a proportion, we can use the formula:

n = (Z^2 * p * q) / E^2

where:

n is the sample size

Z is the z-value corresponding to the desired confidence level (96 percent confidence corresponds to a z-value of approximately 1.75)

p is the estimated proportion (since we don't have an initial estimate, we can assume a conservative estimate of 0.5)

q is 1 - p (complement of the estimated proportion)

E is the desired margin of error (0.02)

Plugging in the values, we have:

n = (1.75^2 * 0.5 * 0.5) / 0.02^2

n ≈ 2627

Therefore, the pollster should survey 2627 voters in order to be 96 percent confident that the true proportion of U.S. voters opposing capital punishment is estimated to within 0.02.

This sample size calculation ensures that the estimate of the true proportion will have a margin of error (E) of 0.02 or less, providing a high level of confidence (96 percent) in the accuracy of the estimate.

In conclusion, by using the formula for sample size estimation, the pollster should survey 2627 voters to achieve a 96 percent confidence level with a margin of error of 0.02 when estimating the true proportion of U.S. voters opposing capital punishment.

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Step-by-step explanation:

v = u + at

v-u = at

a = (v -u)/t

When t = 4, u=10, v=50

a = (50-10)/4

a= 40/4

a = 10

Answer:

Part A: Yes. For every 10 employees, an increase of 80 products produced.

Part B: y = 8x + 120

Part C: Y-intercept indicates the number of products produced when there are 0 employees. The slope indicates the rate of increase of production with the number of employees

Step-by-step explanation:

Part A: 80 - 0 = 80 employees; 760 - 120 = 640 products. Therefore, 640/80 = 8 products per employee or 80 products per 10 employees

Part B: For y = mx + c ,

m = (Y1 - Y0)/(X1 - X0) = (760 - 120)/(80 - 0) = 8

c = Y-intercept, when X = 0. Therefore c = 120

True -  the statement says that a basic variable corresponds to a pivot column in the coefficient matrix. From the definition of basic variables, basic variables correspond to the columns that have a leading 1's (pivot columns).

A mathematical system model based on the use of a linear operator is known as a "linear system" in systems theory. In contrast to nonlinear cases, linear systems often display considerably simpler traits and attributes.

In linear systems, the variables are really only multiplied with constants and then added together; they are never multiplied by each other. In order to express both static and dynamic relationships between variables, linear systems are used.

Something relating to a line is linear. To build a line, all of the linear equations are used. Any equation that doesn't result in a straight line is considered as non. It has a variable slope value and appears as a curve on a graph.

A linear system is one in which both the superposition and homogeneity principles hold true.

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Answer:

find the width and length

Step-by-step explanation:

Answer:

Slope = 3

Explanation:

If we have an equation of the form

then m is the slope and b is the y-intercept.

Now in our case, the equation we have is

Here we identify m = 3. Meaning the slope of the equation is 3.

Answer:

  38 units

Step-by-step explanation:

You want the perimeter of pentagon ABCDE with vertices at A(4, -2), B(4, 10), C(7, 10), D(15, 4), E(7, -2).

The perimeter of a plane figure is the sum of the lengths of its sides.

By counting grid squares, or subtracting coordinates, you can find the lengths of the vertical and horizontal segments easily:

  AB = 12, BC = 3, EA = 3

The lengths of the diagonal segments can be found using the distance formula or your knowledge of Pythagorean triples. Counting grid squares (or subtracting coordinates), you see that each diagonal side has a vertical distance of 6 and a horizontal distance of 8. These correspond to twice the lengths of the sides in a 3-4-5 triangle, so you know the diagonal length is twice the hypotenuse: 2·5 = 10.

The Pythagorean theorem, or the distance formula, will tell you the same thing:

  c² = a² +b² . . . . . . Pythagorean theorem for sides a, b, hypotenuse c

  c = √(a² +b²)

  diagonal length = √(6² +8²) = √100 = 10

Then the remaining two sides are ...

  CD = 10, DE = 10

The perimeter is ...

  perimeter = AB +BC +CD +DE +EA

  = 12 +3 +10 +10 +3 = 38 . . . units

The perimeter of pentagon ABCDE is 38 units.

Answer:

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer:

i know that the first one is correct because its infinite but I'm sorry i don't know the second one. : ( (try the increasing -&,&) tho im not sure

Step-by-step explanation:

Answer:

on the y axis 5 then down 1 over 1 on both sides

Step-by-step explanation:

Answer:

(f o g)(x) =

5x²-15x - 51

Step-by-step explanation:

(f o g)(x) means to wad up g(x) and stuff it into the place of x in f(x).

(f o g)(x)

means f( g(x) )

Here's f(x)

f(x) = 5x - 4

If you were calculating f(2) you would put a 2 in place of x. Or f(18) you would put 18 in place of the x. In this case we will cram the entirety of

x²-3x - 11 into the place of x.

f(x) = 5x + 4

Let's make a lot of room for g(x).

f(x) = 5___x_____ + 4

Okay, here we go:

f(g(x))

= 5(x²-3x - 11) + 4

See how we replace the x in f(x) with the whole entire g(x).

Now we'll simplify because they asked for standard form.



f(g(x))

= 5(x²-3x - 11) + 4

Use distributive property.

= 5x²-15x - 55 + 4

Combine like terms.

= 5x²-15x - 51

(f o g)(x) =

f( g(x) ) = 5x²-15x - 51

Answer:

590mph

Step-by-step explanation:

Speed with wind = 5525÷ 8.5

= 650mph

speed against wind = 4505÷8.5

= 530mph

speed without wind = (650mph+530mph)÷2

= 590mph

The equation that represent the relationship of the coffees is 3x + 5y = 68.

At a coffee shop, two sizes of coffee are sold. A medium coffee costs $3, and a large coffee costs $5.

The equation that represent the relationship between the number of medium coffees sold, x, and the number of large coffees sold, y, in an hour where sales totalled $68 is as follows:

where

Therefore, the equation is as follows:

3x + 5y = 68

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The probability of a single birth resulting in a girl if the probability of a single birth resulting in a boy is 51% is 49%

Probability is the measure of the likelihood of an event occurring. The probability of an event occurring ranges from 0 to 1. If an event is impossible, the probability of its occurrence is 0, and if the event is certain to occur, the probability is 1. The probabilities of the complement of an event equal one minus the probability of the event. For instance, the probability of the complement of an event A, denoted as A', is 1 - P(A). If the probability of an event A is P(A), then the probability of the complement of A is 1 - P(A).

Here, the probability of a single birth resulting in a boy is 51%. Therefore, the probability of a single birth resulting in a girl is the complement of this event, which is 49%. Hence, the main answer is that the probability of a single birth resulting in a girl if the probability of a single birth resulting in a boy is 51% is 49%.

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Answer:

29/36pi radians

240 degrees

Step-by-step explanation:

pi  = 180

145/180pi = 29/36pi radians

4/3*180 = 240 degrees

The correct answer is e. (√3 - 1)/2.

To find the exact value of cos(-π/9), we can use the symmetry property of the cosine function.

The cosine function has a property called evenness, which means that cos(-θ) = cos(θ) for any angle θ.

In this case, we have cos(-π/9). Since the angle is negative, we can rewrite it as -(-π/9), which simplifies to π/9.

So, cos(-π/9) is equal to cos(π/9).

Now, we can determine the exact value of cos(π/9) using trigonometric identities or a calculator.

The exact value of cos(π/9) is (√3 - 1)/2.

Therefore, the correct answer is e. (√3 - 1)/2.

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Step-by-step explanation:

I think you are 100 percent Clear.Thanks

The 95% confidence interval for the difference in the mean distances between oil changes for all luxury cars and all compact lower-price cars is (-94.86, 310.86) miles.

To construct the confidence interval, we use the two-sample t-test with equal variances assumption. We calculate the pooled standard deviation, which is a weighted average of the sample standard deviations based on their degrees of freedom. Then, we compute the standard error of the difference in means using the pooled standard deviation and the sample sizes.

We find the t-value using a t-distribution table with (n1+n2-2) degrees of freedom and a significance level of 0.05. Finally, we construct the confidence interval by adding and subtracting the product of the t-value and the standard error from the difference in sample means. Since the confidence interval includes zero, we conclude that there is no significant difference in the mean distance driven between oil changes for luxury and compact cars.

Therefore, we can infer that the cost of the car is not a significant factor in determining whether people follow the standard recommendation for automobile oil changes.

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Answer:

A- The survey results will be inaccurate because lawns in one neighborhood do not represent all types of lawns in a large city.

Step-by-step explanation:

smile:)