suppose the sum of two intergers is negative. Must both intergers be negative​

Using the Empirical Rule, it is found that 99.7% of the values lie between 76 and 88.

It states that, for a normally distributed random variable:

In this problem, we have that:

99.7% of the values lie within 3 standard deviations of the mean, hence between:

\(82 - 3(2) = 76\)

\(82 + 3(2) = 88\)

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Answer:

x should be 11

Step-by-step explanation:

What we know:

The angles shown are 13x + 12, and 2x + 3

The two angles are complementary, which means they equal 180 degrees.

(13x + 12) + (2x + 3) = 180

15x + 15 = 180

15x = 180 - 15

15x = 165

x = 11

The probability that a woman has endometrial cancer has a partner who smokes is 0.2

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

                                        OR

                                P(A) = n(A)/n(S)

Where,

P(A) is the probability of an event “A”

n(A) is the number of favorable outcomes

n(S) is the total number of events in the sample space.

According to the question,

50 women has endometrial cancer because 5 of them reports that their partner smokes cigerate.

According to the probability formula:

            P(A) = n(A)/ n(s)

                    = 10/50

                    = 0.2

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The statement that proves that angle XWY is equal to angle ZYW is

A. If two parallels are cut by a transverse, then alternate interior angles are congruent

Alternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.

When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.

In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles

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Answer:

25, 34, 43

Step-by-step explanation:

-11 + x = -2, -11 + 9 = -2                -2 + x = 7, -2 + 9 = 7,  7 + 9 = 16                             -2 - x = -11, -2 - 9 = -11                   7 - x = - 2,                                                               2 + x = 11,  11 - 2 = 9, 9 = x            7 - 7 = 0 - 2 = -2,   7 + 2 = 9,    7 - 9 = -2    

16 + 9 = 25,   25 + 9 = 34,   34 + 9 = 43              

J'espère que cela pourra aider : )                                                    

The storm rainfall flux is 0.00127 m2/hr, 1.27 kg liquid water/m2hr, 2.8 lb liquid water/m2hr, 1.27 liters liquid water/m2hr, and 0.335 gallons liquid water/m2hr. The amount of liquid water fell on the garden is 80.6 L, 21.3 gallons.

Dimensions of outdoor vegetable garden = 2 m × 2 m

Storm rainfall = 0.8 inches of rain

Time of storm = 1 hr(

a) The rainfall flux is the amount of rainfall per unit area and unit time. It is given as:

Rainfall flux = (Amount of rainfall) / (Area × Time)

Given the area of the garden is 2 m × 2 m, and the time is 1 hr, the rainfall flux is:

Rainfall flux = (0.8 inches of rain) / (2 m × 2 m × 1 hr)

Converting inches to meters, we get:

1 inch = 0.0254 m

Therefore,

Rainfall flux = (0.8 × 0.0254 m) / (2 m × 2 m × 1 hr) = 0.00127 m/hr

Converting the rainfall flux to other units:

In kg/hr:

1 kg of water = 1000 g of water

Density of water = 1000 kg/m3

So, 1 m3 of water = 1000 kg of water

So, 1 m2 of water of depth 1 m = 1000 kg of water

Therefore, 1 m2 of water of depth 1 mm = 1 kg of water

Therefore, the rainfall flux in kg/hr = (0.00127 m/hr) × (1000 kg/m3) = 1.27 kg/m2hr

In lbs/hr:

1 lb of water = 453.592 g of water

So, the rainfall flux in lbs/hr = (0.00127 m/hr) × (1000 kg/m3) × (2.20462 lb/kg) = 2.8 lbs/m2hr

In liters/hr:

1 m3 of water = 1000 L of water

So, 1 m2 of water of depth 1 mm = 1 L of water

Therefore, the rainfall flux in L/hr = (0.00127 m/hr) × (1000 L/m3) = 1.27 L/m2hr

In gallons/hr:

1 gallon = 3.78541 L

So, the rainfall flux in gallons/hr = (0.00127 m/hr) × (1000 L/m3) × (1 gallon/3.78541 L) = 0.335 gallons/m2hr

(b) To calculate the amount of water that fell on the garden, we need to calculate the volume of water.

Volume = Area × Depth.

The area of the garden is 2 m × 2 m.

We need to convert the rainfall amount to meters.

1 inch = 0.0254 m

Therefore, 0.8 inches of rain = 0.8 × 0.0254 m = 0.02032 m

Volume of water = Area × Depth = (2 m × 2 m) × 0.02032 m = 0.0806 m3

Converting the volume to other units:

In liters:

1 m3 of water = 1000 L of water

Therefore, the volume of water in liters = 0.0806 m3 × 1000 L/m3 = 80.6 L

In gallons:

1 gallon = 3.78541 L

Therefore, the volume of water in gallons = 80.6 L / 3.78541 L/gallon = 21.3 gallons.

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the maximum volume of a cone that can be carved from the foam cylinder is 6 cubic inches. Rounded to the hundredths place, this is 28.27 in3.

To find the maximum volume of a cone that can be carved from the foam cylinder, we need to first determine the dimensions of the largest possible cone that can be carved.The base of the cone must fit within the circular base of the cylinder, so the maximum diameter of the base of the cone is 3 inches.

The height of the cone must be less than or equal to the height of the cylinder, which is 8 inches.

V = (1/3)πr^2h

where V is the volume, π is pi (approximately 3.14), r is the radius of the base (half the diameter), and h is the height.

In this case, r = 1.5 inches and h ≤ 8 inches.

Substituting these values into the formula, we get:

V = (1/3)π(1.5)^2h

Simplifying, we get:

V = (1/3)(3.14)(2.25)h

V = 0.75h
The maximum value of h is achieved when the height of the cone is equal to the height of the cylinder, which is 8 inches. Substituting this value into the formula, we get:

V = 0.75(8)

V = 6

Therefore, the maximum volume of a cone that can be carved from the foam cylinder is 6 cubic inches. Rounded to the hundredths place, this is 28.27 in3.

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The percentage of the scheduled time lost was 16.7%

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.

Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. It is given by:

Percentage = (value / total value) * 100%

Time stopped = 35 mins

Scheduled time = 3 1/2 hour

converting to mins

3 1/2 hour = 210 mins

% lost = (35/210) x 100

% lost = 16.7%

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The cost of each item is as follows: Each book costs $5.33, and each folder costs $1.73.

We know that Dawn spent a total of $26.50, including sales tax, on the books and folders. This means that the cost of the books and folders, before including sales tax, is less than $26.50.

Each book costs $5.33. Since Dawn bought 4 books, the total cost of the books without sales tax can be calculated by multiplying the cost of each book by the number of books:

=> $5.33/book * 4 books = $21.32.

We are also given that the total sales tax paid was $1.73. This sales tax is calculated based on the cost of the books and folders.

To determine the sales tax rate, we need to divide the total sales tax by the total cost of the books and folders:

=> $1.73 / $21.32 = 0.081, or 8.1%

To find the cost of each item, we need to allocate the total cost of $26.50 between the books and the folders. Since we already know the total cost of the books is $21.32, we can subtract this from the total cost to find the cost of the folders:

=> $26.50 - $21.32 = $5.18.

Finally, we divide the cost of the folders by the number of folders to find the cost of each folder:

=> $5.18 / 3 folders = $1.7267, or approximately $1.73

So, the cost of each item is as follows: Each book costs $5.33, and each folder costs $1.73.

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Answer:

32 in²

Step-by-step explanation:

length ratio = \(\frac{12}{18}\) = \(\frac{2}{3}\)

area ratio = (\(\frac{2}{3}\) )² = \(\frac{4}{9}\)

smaller area = 72 × \(\frac{4}{9}\) = 8 × 4 = 32 in²

The area of the smaller shaded triangle is approximately 31.98 square inches.

The area of a triangle is given by the formula: A = 1/2 * base * height. In an isosceles trapezoid, the two parallel sides are equal in length. In this case, the base lengths of the trapezoid are 12 inches and 18 inches.

To find the area of the larger shaded triangle, we need to determine its base and height.

The base of the larger shaded triangle is the same as the length of the larger base of the trapezoid, which is 18 inches.

Let's denote the height of the larger shaded triangle as h1. Using the formula for the area of a triangle, we have: 72 = 1/2 * 18 * h1 To solve for h1, we can multiply both sides of the equation by 2 and divide by 18: 2 * 72 = h1 h1 = 144 / 18 h1 = 8 inches

So, the height of the larger shaded triangle is 8 inches. Now, let's find the area of the smaller shaded triangle. The base of the smaller shaded triangle is the same as the length of the smaller base of the trapezoid, which is 12 inches. Let's denote the height of the smaller shaded triangle as h2. Using the formula for the area of a triangle, we have: A = 1/2 * base * height A = 1/2 * 12 * h2

We don't know the value of h2, but we do know that the two shaded triangles are similar because they have equal angles. This means that the ratio of the heights of the two triangles is the same as the ratio of their bases. The ratio of the bases of the two triangles is 18/12 = 3/2.

So, the ratio of the heights of the two triangles is also 3/2.

To find the height of the smaller shaded triangle, we can set up a proportion: h2 / 8 = 2/3 Cross-multiplying, we have: 3 * h2 = 8 * 2 3 * h2 = 16 h2 = 16 / 3 h2 = 5.33 (rounded to two decimal places)

So, the height of the smaller shaded triangle is approximately 5.33 inches.

Now, we can find the area of the smaller shaded triangle using the formula: A = 1/2 * base * height A = 1/2 * 12 * 5.33 A = 31.98 square inches (rounded to two decimal places)

Therefore, the area of the smaller shaded triangle is approximately 31.98 square inches.

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To find a quadratic equation with the y-intercept and vertex, follow these steps: identify the coordinates of the y-intercept and vertex, substitute them into the general form of the quadratic equation, solve for the coefficients, and substitute the coefficients back into the equation. For example, if the y-intercept is (0, 3) and the vertex is (-2, 1), the quadratic equation would be y = x^2 + x + 3.

To find a quadratic equation with the y-intercept and vertex, we can follow these steps:

For example, let's say the y-intercept is (0, 3) and the vertex is (-2, 1). We can substitute these coordinates into the general form of the quadratic equation:

3 = a(0)^2 + b(0) + c

1 = a(-2)^2 + b(-2) + c

Simplifying these equations, we get:

c = 3

4a - 2b + c = 1

By substituting c = 3 into the second equation, we can solve for a and b:

4a - 2b + 3 = 1

4a - 2b = -2

2a - b = -1

By solving this system of equations, we find a = 1 and b = 1. Substituting these values back into the general form of the quadratic equation, we obtain the final equation:

y = x^2 + x + 3

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To find a quadratic equation with a given y-intercept and vertex, you need the coordinates of the vertex and one additional point on the curve.

Example:

Suppose we want to find a quadratic equation with a y-intercept of (0, 4) and a vertex at (2, -1).

To find a quadratic equation with a given y-intercept and vertex, you can use the vertex form of a quadratic equation and substitute the coordinates to obtain the equation. Then, use the y-intercept to find an additional point on the curve and solve a system of equations to determine the coefficients. Finally, substitute the coefficients into the standard form of the quadratic equation to get the final equation.

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Answer:

1 1/2

Step-by-step explanation:

1.) First find the common denominator of the 2 fractions (8)    4: 4

    8: 4, 8

2.) then you write a new expression with the numerator left blank and the denominator as 8 shown below in the step by step explanation.  /8 + /8

3.)3/8 + 2/4 multiply by 1 both numerator and denominator for the first fraction. And multiply by 2 both numerator and denominator for the second fraction. 3/8 + 4/8.

4.) Then you add those 2 fractions which I assume you already know how by adding the numerators together, and get 12/8.

5.) You simplify 12/8 and get 1 4/8. 4/8 is equal to 1/2 so its 1 1/2.

Answer:

a. h=5
b. A=.5(b)(h). So, 18=.5(6)(h+1). If I plug in 5 as h and solve, 18=.5(6)(6) which can be simplified to 18=(.5)(36). So, h is 5.  

Step-by-step explanation:

Since the area = 18, and the formula for area is .5(b)(h), I can start solving by plugging in the numbers I have. 18=.5(6)(h+1). I multiply both sides by 2 to get rid of the .5, getting 36=6(h+1). I divide by 6 on both sides, getting 6=h+1. I subract 1 on both sides to get h=5

Answer:

a. h=5

b. A=.5(b)(h)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Rewrite the equation as  

8(y+4)=m

Divide each term in 8(y+4)=m by 8

and simplify

y+4=\(\frac{m}{8}\)

Subtract  

4 from both sides of the equation

y=\(\frac{m}{8}\)−4

The statement is proved that "(u,v) = 3u_1​v_1​+5u_2​v_2​ defines an inner product on R2"

An inner product is defined as a binary operation that takes two vectors from a vector space and returns a scalar value.

It satisfies some axioms like linearity, symmetry, and positive-definiteness.

The following are the axioms that an inner product must satisfy.

(i) Positivity: ∀x∈V,⟨x,x⟩≥0.

(ii) Definiteness: ⟨x,x⟩=0⟹x=0.

(iii) Linearity: ∀x,y,z∈V,α,β∈F,⟨αx+βy,z⟩=α⟨x,z⟩+β⟨y,z⟩.

(iv) Conjugate symmetry: ∀x,y∈V,⟨x,y⟩ = ⟨y,x⟩.

Now, let us check the axioms one by one on (u,v) = 3u_1v_1 + 5u_2v_2.

Let u = (u_1, u_2), v = (v_1, v_2), and w = (w_1, w_2) be arbitrary vectors in R2 and a, b ∈ R.

(i) Positivity: (u, u) = 3(u_1)² + 5(u_2)² ≥ 0 for all u ∈ R².

(ii) Definiteness: (u, u) = 3(u_1)² + 5(u_2)² = 0 only if u_1 = u_2 = 0.

(iii) Linearity:

(a u + b v, w) = 3(a u_1 + b v_1) w_1 + 5(a u_2 + b v_2) w_2

                     = a (3 u_1 w_1 + 5 u_2 w_2) + b (3 v_1 w_1 + 5 v_2 w_2)

                     = a (u, w) + b (v, w).

(iv) Conjugate symmetry:

(u, v) = 3u_1 v_1 + 5u_2 v_2

       = 3v_1 u_1 + 5v_2 u_2

       = (v, u).

Since all the axioms of an inner product are satisfied by the expression (u,v) =3u_1v_1+5u_2v_2, thus it is a valid inner product.

Therefore, the statement is proved.

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Answer:

A NOT C

Step-by-step explanation:

JKHMDSVCJDSAHVCDSVCJDSHG

Applying the altitude theorem and the Pythagorean theorem, the length of line segment BC to the nearest tenth is: C. 31.2 units

Recall:

First find DC using the altitude theorem:

x = DC

y = 5 units

h = 12 units

12 = √(5×DC)

12² = 5(DC)

144/5 = DC

DC = 28.8

Considering right triangle BDC, use Pythagorean theorem to find BC:

BC = √(DC²+BD²)

BC = √(28.8²+12²)

BC = 31.2 units

In summary, applying the altitude theorem and the Pythagorean theorem, the length of line segment BC to the nearest tenth is: C. 31.2 units

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The combination can be

A factor is a number that is multiplied by another number to produce the desired result. The answer to a multiplication puzzle is a product. Imagine multiplying the factors in a multiplication problem to get the answer. For instance, the factors 2 and 4 add up to 8: Just two factors or a great many factors can affect a number.

Total Number of Factors for N = (a+1) (b+1) (c+1) is the formula for the total number of factors for a given number.

given:

Type               Number of muffins

blueberry              40

Chocolate              48

Strawberry             32

So, muffins need to be divided equally into separate gift baskets with the same number of each type of muffins in each basket.

The possible condition can be

2 gift basket

20 Blueberry, 24 chocolate, 16 strawberry

4 gift basket

10 Blueberry, 12 chocolate, 8 strawberry

6 gift basket

5 Blueberry, 6 chocolate, 4 strawberry

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Answer:

we know that

area of the circle is equal to

A=pi* r^{2}A=pi∗r

2

solve for r

r= \sqrt{ \frac{A}{pi}}r=

pi

A

for A=60 cm^{2}60cm

2

r= \sqrt{ \frac{60}{pi}} cmr=

pi

60

cm

we know that

\begin{gathered} \sqrt{60} = \sqrt{ 2^{4}*3*5} \\ =2 \sqrt{15} \end{gathered}

60

=

2

4

∗3∗5

=2

15

so

\sqrt{ \frac{60}{pi}}=2 \sqrt{ \frac{15}{pi}}

pi

60

=2

pi

15

2 \sqrt{ \frac{15}{pi}}=2 \frac{ \sqrt{15}}{ \sqrt{pi}} * \frac{ \sqrt{pi}}{ \sqrt{pi}}2

pi

15

=2

pi

15

∗

pi

pi

=2 \frac{ \sqrt{15pi}}{pi} cm=2

pi

15pi

cm

the answer is

2 \frac{ \sqrt{15pi}}{pi} cm2

pi

15pi

cm

Answer:

−49  / 8

decimal form- -6.125

Step-by-step explanation:

140−  167  / 8  (7)

=

140−  1169  / 8

=

−49  / 8

The required, expression -7 + 24i with the form a + bi, we can see that the value of b is 24.

To find the value of b in the expression (3 + 4i)^2, we can simply expand the expression and identify the coefficient of the imaginary part.

(3 + 4i)² = (3 + 4i)(3 + 4i)

Using the FOIL method, we can multiply the terms:

= 3 * 3 + 3 * 4i + 4i * 3 + 4i * 4i

= 9 + 12i + 12i + 16i²

Since i² is defined as -1, we can substitute it:

= 9 + 12i + 12i - 16

= -7 + 24i

Comparing the expression -7 + 24i with the form a + bi, we can see that the value of b is 24.

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Complete question:

(3+4i)²

if the expression above is written in the form a+ bi, where a and b are real numbers, what is the value of b?

Answer:

44

Step-by-step explanation:

base(b) = 11, height(h) = 8, Area of parallelogram = ? We know that, Area of parallelogram = 1/2 × b× h = 1/2 × 11 × 8 = 11 × 4 = 44 square units

The answer is 88


11x8 = 88 base times height !!!!

By solving the equation we know that 15 players can be brought to the tournament.

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.

For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.

So, we know that:

Softball players raised $1186.50 to attend a tournament.

They allocated $21.50 for meals per player and paid $842.50 for the bus rental.

We must apply the following calculation to determine the total number of players they are permitted to bring:

Formula: Total amount of money= fixed cost + unitary variable cost × number of players

1186.50 = 842.50 + 21.50 × number of players

1186.50 - 842.50 = 21.50 × number of players

344/21.50 = number of players

15 = Number of players

Therefore, by solving the equation we know that 15 players can be brought to the tournament.

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Answer:

a) -11

b) 75

Step-by-step explanation:

a= -24-13=-11

b= 61-(-14)=75

Given a Math exam with 7 short answer questions and Peter intending to answer three of them, there are a total of 35 different combinations of short answer questions he can choose.

To determine the number of combinations, we can use the concept of combinations in combinatorics. The formula for combinations is given by:

C(n, r) = n! / (r! * (n - r)!)

Where:

C(n, r) represents the number of combinations of choosing r items from a set of n items.

n! denotes the factorial of n, which is the product of all positive integers up to n.

In this case, Peter wants to answer three out of the seven questions, so we can calculate it as:

C(7, 3) = 7! / (3! * (7 - 3)!) = 7! / (3! * 4!)

Simplifying further:

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1

3! = 3 * 2 * 1

4! = 4 * 3 * 2 * 1

C(7, 3) = (7 * 6 * 5 * 4 * 3 * 2 * 1) / [(3 * 2 * 1) * (4 * 3 * 2 * 1)]

After canceling out common terms, we get:

C(7, 3) = 7 * 6 * 5 / (3 * 2 * 1) = 35

Therefore, there are 35 different combinations of short answer questions Peter can choose to answer.

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The best way to compare exam score to the number of hours of sleep is by

Histogram, you can easily determine the score using the bars on the histogram at every hours of sleep.

Scatter

Answer:

3:10

Step-by-step explanation:

The GCF of 12 and 40 is 4.

\(12:40 = 12/4:40/4 = \boxed{3 : 10}\)

Hope this helps.

Therefore, there are 15,504 different samples possible when choosing 5 chips from a batch of 20 semiconductor chips.

To determine the number of different samples possible when choosing 5 chips from a batch of 20 semiconductor chips, we can use the combination formula. The number of different samples (denoted as C(n, k)) can be calculated using the formula:

C(n, k) = n! / (k!(n - k)!)

where n represents the total number of chips and k represents the number of chips in the sample.

In this case, we have:

n = 20 (total number of chips)

k = 5 (number of chips in the sample)

Using the formula, we can calculate the number of different samples:

C(20, 5) = 20! / (5!(20 - 5)!)

Calculating this value, we find that:

C(20, 5) = 15,504

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The required cubic polynomial is

f(x) = \(-2x^3-2x^2-28x+48\)

What is a polynomial?

An algebraic expression of the form \(a_0 + a_1x+ .... + a_nx^n\) (\(a_0 \neq 0\)) is called a polynomial of degree n.

The zeroes of the cubic polynomial are -4, 2, 3

Let the cubic polynomial is

f(x) = a(x - (-4))(x - 2)(x - 3)

f(x) = a(x + 4)(x - 2)(x - 3)

If x = -5, f(x) = 112

112 = a(-5 + 4) (-5 - 2)(-5 - 3)

112 = -56a

a = \(-\frac{112}{56}\)

a = -2

f(x) = -2(x+ 4)(x - 2)(x - 3)

\(f(x) = -2(x+ 4)(x^2 -3x -2x +6)\\f(x) = -2(x + 4)(x^2 - 5x + 6)\\f(x) = -2(x^3 - 5x^2+4x^2+6x - 20x+24)\\f(x) = -2(x^3 - x^2 - 14x +24)\\f(x) = -2x^3 -2x^2 - 28x + 48\)

(x +4)(x - 2)(x - 3)

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