How many solutions are there to the equation
- x ^ 2 + 5 = 10

A-0
B-1
C-2
D-infinite

Answer:

1/ Heidi earned $61.20 in commission

2/ The jewelry store makes $618.80 from hers sales

Step-by-step explanation:

9% = 0.09

First, take 680 times 0.09 = $61.20

Heidi earned $61.20 in commission

For the second question

Take 680 - 61.20 = $618.8

The jewelry store makes $618.80 from its sales

Answer:

Consider the following graph

(a) Find the interval(s) on which fis increasing. (Enter your answer using interval notation.)  = (1,3)U(4,6).

(b) Find the interval(s) on which fis decreasing. (Enter your answer using interval notation.) = (0,1)U(3,4).

(c) Find the open interval(s) on which fis concave upward. (Enter your answer using interval notation.) = (0,2).

(d) Find the interval(s) on which fis concave downward. (Enter your answer using interval notation.) = (2,4)U(4,6).

(e) Find the coordinates of the point(s) of inflection. (x,y)

=  (2, 3), (4, 1)

The graph of the derivative f' of a function fis shown.

(a) on what intervals is f increasing? (Enter your answer using interval notation.) = (0,1)U(3,5)

(b) On what intervals is f decreasing? (Enter your answer using interval notation.) = (1,3)U(5,6)

(c) At what values of x does f have a local maximum or local minimum? (Enter your answers as a comma-separated list.) = 1,3,5

a. In a random sample of 1,000 births, the expected number of births that take place by Caesarian section is:

E(X) = n*p = 1,000 * 0.32 = 320 births

Therefore, on average, 320 births out of 1,000 will take place by Caesarian section.

b. The variance of the number of Caesarian section births in a sample of 1,000 births is:

Var(X) = np(1-p) = 1,000 * 0.32 * (1-0.32) = 217.60

The standard deviation is the square root of the variance:

SD(X) = sqrt(Var(X)) = sqrt(217.60) = 14.76

Therefore, the standard deviation of the number of Caesarian section births in a sample of 1,000 births is 14.76.

c. To form an interval that is likely to contain the number of Caesarian section births in a sample of 1,000 births, we can use the normal distribution and the central limit theorem. Since n*p = 320 is greater than 10, we can assume that the distribution of the number of Caesarian section births in a sample of 1,000 births is approximately normal.

The 95% confidence interval for the number of Caesarian section births is:

320 ± 1.96*(14.76) = (291.16, 348.84)

Therefore, we can be 95% confident that the number of Caesarian section births in a sample of 1,000 births will be between 291 and 349.

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━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

So you already know that 34 is 34 stories in length.

Positive means: up, forward

Negative means: down, backward

Since the elevator is going down 34 stories, it is negative.

An elevator ride down 34 stories can be represented as -34 or negative 34.

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

The required  integer is -34.

It is required to find the integer.

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Zero is not a fraction or decimal of any number. It is neither positive nor negative.

Given:

Positive means: up, forward

Negative means: down, backward

Since the elevator is going down, the situation is represented by a negative integer. Since it goes down 34 stories, then it is represented by the integer −34.

Therefore, the required  integer is -34.

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Answer:

there is no multiplication, so just 29+ 19b

Answer: i solved it for you, but all you have to do is add this 19b + 29

Step-by-step explanation:

I really hope this helps!! Have an amazing day!! :)

A polynomial function of degree 3 with real coefficients that has the given zeros -2, 3, and -6 is f(x) = \(x^{3}\) + 5\(x^{2}\) - 42.

The zeros of a polynomial function are the values of x for which the function evaluates to zero. Since we are given the zeros -2, 3, and -6, we can express the polynomial function as the product of factors corresponding to each zero.

To find the polynomial, we use the fact that if a number is a zero of a polynomial, then the corresponding factor is equal to zero. So, for the zeros -2, 3, and -6, we have the factors (x + 2), (x - 3), and (x + 6), respectively.

Multiplying these factors together, we get:

f(x) = (x + 2)(x - 3)(x + 6)

Expanding the expression further:

f(x) = (\(x^{2}\) - x - 6)(x + 6)

= (\(x^{2}\) - x - 6)(x) + (\(x^{2}\) - x - 6)(6)

= \(x^{3}\) - \(x^{2}\) - 6x + 6\(x^{2}\) - 6x - 36

= \(x^{3}\) + 5\(x^{2}\) - 42

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(a)An function the deformation gradient F is F = 1 γ 0,0 2X2 0,0 0 1

(b The right Cauchy-Green deformation tensor C is C = 1+γ²γ 0,

γ 4X2²0,0 0 1 the left Cauchy-Green deformation tensor B is B = 1+γ² γ 0,γ γ²+4X2² 0,0 0 1.

(a) Deformation Gradient F:

The deformation gradient is defined as the derivative of the deformed coordinates x with respect to the initial coordinates X:

F = ∂x/∂X

Given the shear deformation x = φ(X) with x1 = X1 + γX2, x2 = X2X2, and x3 = X3, we can compute the deformation gradient as follows:

F =∂x1/∂X1 ∂x1/∂X2 ∂x1/∂X3

∂x2/∂X1 ∂x2/∂X2 ∂x2/∂X3

∂x3/∂X1 ∂x3/∂X2 ∂x3/∂X3

Taking the partial derivatives:

∂x1/∂X1 = 1, ∂x1/∂X2 = γ, ∂x1/∂X3 = 0

∂x2/∂X1 = 0, ∂x2/∂X2 = 2X2, ∂x2/∂X3 = 0

∂x3/∂X1 = 0, ∂x3/∂X2 = 0, ∂x3/∂X3 = 1

(b) Right and Left Cauchy-Green Deformation Tensors C and B:

The right Cauchy-Green deformation tensor C is defined as the square of the deformation gradient:

C = F²T × F

The left Cauchy-Green deformation tensor B is defined as the square of the transpose of the deformation gradient:

B = F × F²T

Calculating C:

C = F²T × F

C = 1 0 0

γ 2X2 0

0 0 1

1 γ 0

0 2X2 0

0 0 1

C =1+γ² γ 0

γ 4X2² 0

0 0 1

Calculating B:

B = F × F²T

B = 1 γ 0

0 2X2 0

0 0 1

1 0 0

γ 2X2 0

0 0 1

B = 1+γ² γ 0

γ γ²+4X2² 0

0 0 1

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We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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The probability of your friend picking a striped ball has changed based on your action of picking a solid ball without replacement, the events are not independent.

In this scenario, you have a bag with 14 billiard balls, consisting of 7 solids and 7 stripes. The events in question are you picking a solid ball and your friend picking a striped ball. These events are considered independent if the occurrence of one event does not affect the probability of the other event.

Since you are not replacing the ball you picked, the total number of balls in the bag changes. If you pick a solid ball, the remaining balls in the bag will be 6 solids and 7 stripes, making a total of 13 balls. In this case, the probability of your friend picking a striped ball is 7/13, instead of the original 7/14.

As the probability of your friend picking a striped ball has changed based on your action of picking a solid ball without replacement, the events are not independent. The outcome of your pick has an influence on the probability of your friend's pick in this scenario.

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Answer:

Let A be the event of me randomly picking a solid. Let B be the event of my friend randomly picking a stripe. These two events are independent if any one of the following conditions is true:

P (A|B) = P (A), P(B|A) = P(B), or P(A and B) = P(A) X P(B).

P(A) = 7/14 = 1/2

P(B) = 7/14 = 1/2

The probability of getting a solid and then a stripe (without replacement) is:

P (A⋂B) = 7/14 X 7/13 = 7/26

P (A⋂B) ≠ P(A) X P(B).

So, the two events are dependent.

plato

Answer:

Step-by-step explanation:

The point-slope form of the equation is y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through and m is the slope:

m = -⁵/₂

(-4, -2)    ⇒   x₀ = -4,  y₀ = -2

The point-slope form of the equation:

y + 2 = -⁵/₂(x + 4)

So:

y + 2 = -⁵/₂x - 10         {subtract 2 from both sides}

y = -⁵/₂x - 12             ←  the slope-intercept form of the equation

The total area of the figure is 132 cm².

Notice that on the top rectangle we can input the little triangle in the left side on the "hole" in the right side.

Then we have two rectangles:

One is 22cm by 3.5cm

One is 22cm by 2.5cm

The area is just the product of these dimensions, we will get that the areas are:

a₁ = 22cm*3.5cm = 77cm²

a₂ = 22cm*2.5cm = 55cm²

The total area is 77cm + 55cm = 132 cm²

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Area of square = Side × Side

⇛Area = 120 cm × 120 cm

⇛Area = 14400 cm²

Hence , the area of square is 14400 cm²

Answer:

14400

Step-by-step explanation:

Area for square formula: B × H

Since a square has equal sides for each side, you will multiply 120 by itself.

120 × 120 = 14400

The area of the square is 14400.

Hope this helped.

To calculate (f-g)(x) we simply subtract g from f and the organize the powers in descending order

we get

So (f-g)(x) = x^2-14x+33

The absolute value is defined as

\(|x|=\begin{cases}x&\text{if }x\ge0\\-x&\text{if }x<0\end{cases}\)

So for example, if x = 3, then |x| = |3| = 3, since 3 is positive. On the other hand, if x = -5, then |x| = |-5| = -(-5) = 5, since -5 is negative. The absolute value is always positive.

For the inequality |7 + 8x| > 5, you consider the two cases where the argument to the absolute value (the expression you find inside the bars) is either positive or negative.

• If 7 + 8x ≥ 0, then |7 + 8x| = 7 + 8x, so that

\(|7+8x|>5\implies 7+8x>5 \implies 8x>-2 \implies x>-\dfrac14\)

• Otherwise, if 7 + 8x < 0, then |7 + 8x| = -(7 + 8x), so that

\(|7+8x|>5\implies-(7+8x)>5\implies7+8x<-5\implies8x<-12\implies x<-\dfrac32\)

The solution to the inequality is the union of these two intervals.

The  trains are side by side after approximately 15 seconds.Option (b) is correct.

The position of the first train is given by the function:

\($$y_1 = 14t^2$$\)

The position of the second train is given by the function:

\($$y_2 = 130t + 1200$$\)

To find the time when the trains are side by side, we need to solve for the value of t that makes y1 = y2. Thus, we can set the two equations equal to each other:

\($$14t^2 = 130t + 1200$$\)

Rearranging the terms, we get:

\($$14t^2 - 130t - 1200 = 0$$\)

Dividing both sides by 2 to simplify the coefficients, we get:

\($7t^2 - 65t - 600 = 0$$\)

We can use the quadratic formula to solve for t:

\($t = \frac{-(-65) \pm \sqrt{(-65)^2 - 4(7)(-600)}}{2(7)} = \frac{65 \pm \sqrt{4225 + 16800}}{14}$$\)

Simplifying the expression under the square root, we get:

\($$\sqrt{21025} = 145$$\)

So the solutions are:

\($t_1 = \frac{65 + 145}{14}=15$$\)

\($t_2 = \frac{65 - 145}{14} \approx -5.71$$\)

Since time cannot be negative, we discard t2 as an extraneous solution. Thus, the viable time when the trains are side by side is:

\($t = t_1 =15$$\)

Therefore, the trains are side by side after approximately 15 seconds.

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Answer:

Step-by-step explanation:

1. Square

2. Rhombus

3. Trapezoid

4. Diamond

5. Octogon

6. Triangle

7. Pentagon

8. Hexagon

9. Triangle?

Answer: 87.6719183867

Step-by-step explanation:

Exact Form: √ 7686.3652736

Decimal Form: 87.67191838 …

Step-by-step explanation: The radical cannot be simplified, but it can be approximated.

Give me brainliest or a thank you pls :)

From.the calculated area and perimeter of the field, it will cost the farmer $475740 to fence and seed the pasture.

The area of the field is calculated as follows:

Area of square = 450 ft × 450 ft = 202500 square feet

Area of triangle = (450 ft × 120 ft)/2 = 27000 square feet

Area of field = 229500 square feet

Cost of seeding the field = 229500 × $2 = $459000

Perimeter of the field = 450 + 450 + 450 + 255 + 255 = 1860 ft

1 ft = 1/3 yard

1860 ft = 1860 × 1/3 yards = 620 yards

Cost of fencing = 620 × $27 = $16740

Total cost of seeding and fencing = $475200

Therefore, it will cost the farmer $475740 to fence and seed the pasture.

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Answer:

416

Step-by-step explanation:

The value of the number is 57/16

The mathematical statement is given as:

Nine times a number y subtracted from 85 is seven times the sum of four and y

Remove the above mathematical statement as an algebraic expression

85 - 9y = 7(4 + y)

Open the bracket

85 - 9y = 28 + 7y

Collect the like terms

9y + 7y = 85 - 28

Evaluate the like terms

16y = 57

Divide both sides by 16

y = 57/16

Hence, the value of the number is 57/16

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Nearly 1,659 feet of granite was tunnelled through to make tunnel no. 6 through the sierra Nevada mountains.

Early snowfall prevented the Central Pacific from starting construction on Tunnel No. 6, or the Summit Tunnel, in August 1865. It was built using a variety of engineering and construction methods and was located more than seven thousand feet above sea level.

When the workmen finally broke through, they discovered that they were only two inches off from the calculations that were used to locate its end points and central shaft. The length of the tunnel that was built through the Sierra Nevada mountains is therefore given as nearly 1,659 feet of granite was tunnelled through to make tunnel no. 6 through the Sierra Nevada mountains.

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8,8,8 este primull!!!!!!! sper că te-am ajutat

Answer:

c is the and

no worries thank you to each of the Fourth of that mother you have any other questions please contact me

a) To find the sales 3 weeks after the end of the promotion, we can substitute the value of 3 into the given sales decay equation:

S = 295,000 * e^(-0.3*3)

S = 295,000 * e^(-0.9)

Using a calculator or software, we can evaluate this expression:

S ≈ 295,000 * 0.40657

S ≈ 119,892.15

Therefore, the sales 3 weeks after the end of the promotion is approximately $119,892.15.

b) To find the number of weeks after the end of the promotion when sales drop below $25,000, we can set up the sales decay equation and solve for the number of weeks:

25,000 = 295,000 * e^(-0.3t)

Dividing both sides by 295,000:

0.08475 = e^(-0.3t)

Taking the natural logarithm of both sides:

ln(0.08475) = -0.3t

Solving for t:

t = ln(0.08475) / -0.3

Using a calculator or software, we can evaluate this expression:

t ≈ 9.28

Therefore, if no new campaign is started, the sales will drop below $25,000 approximately 9.28 weeks after the end of the promotion.

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\( \star\:{\underline{\underline{\sf{\purple{Given ::}}}}}\)

❖ \(\sf a_{5} + a_{9} = 72 \)

❖ \(\sf a_{7} + a_{12}= 97 \)

\( \star\:{\underline{\underline{\sf{\purple{To \: Find ::}}}}}\)

❖ The A.P

\( \star\:{\underline{\underline{\sf{\purple{Solution ::}}}}}\)

Let,

\(a\) be the first term and \(d\) be the common difference of the A.P

According to the question,

\(\sf a_{5} + a_{9} = 72 \) and \(\sf a_{7} + a_{12}= 97 \)

\(\longrightarrow \sf (a + 4d) + (a + 8d) = 72\) and \(\sf (a + 6d) + (a + 11d) = 97\)

Thus, we have

\( \longrightarrow \sf 2a + 12d = 72 - - (i)\)

\( \longrightarrow \sf 2a + 17d = 97 - - (ii) \)

Subtracting (i) from (ii), we get

\( \implies \sf 5d = 25\)

\( \implies \sf d = \dfrac{25}{5} \)

\(\implies {\star{ \underline{\boxed{\sf{\pink{\sf d = 5}}}}}}\)

Now,

Putting d=5 in (i), we get

\( \longrightarrow \sf 2a + 12(5) = 72 \)

\( \longrightarrow \sf 2a + 60= 72 \)

\(\longrightarrow \sf 2a= 72 - 60\)

\(\longrightarrow \sf 2a= 12\)

\(\longrightarrow \sf a= \dfrac{12}{2} \)

\(\longrightarrow{\star{ \underline{\boxed{\sf{\pink{\sf a = 6}}}}}}\)

\( \therefore\) a=6 and d=5

Hence, the A.P is 6,11,16,21,26...

\(\rule{250pt}{2.5pt}\)

Step-by-step explanation:

Given

\(1953125=5^9\)

For a perfect square, its square root must be an integer

The square root of 1953125 i.e. \(\sqrt{1953125}=\sqrt{5^9}\)

or, \(\sqrt{5^9}=5^\frac{9}{2}\)

Clearly,  \(\frac{9}{2}\) is not an integer so, \(5^{\frac{9}{2}}\) is also not an integer

Hence, 1953125 is not a square number

(a) The falsity of p can be justified by providing evidence or logical reasoning that disproves the statement.(b) The statement is false if there is no integer k that satisfies m = kn - 1. (c) The equation x²= 0 has solutions if and only if x is equal to 0. d)  if p is stated to be prime, it means that p is a positive integer greater than 1 that has no divisors other than 1 and itself.

(a) To determine the falsity of a statement, we need to examine the logical reasoning or evidence provided. If the statement contradicts established facts, theories, or logical principles, then it can be considered false. Justifying the falsity involves presenting arguments or counterexamples that disprove the statement's validity.

(b) When evaluating the truthfulness of the statement "If m is an integer belonging to N with -1 modulo n," we must assess whether there exists an integer k that satisfies the given condition. If we can find at least one counterexample where no such integer k exists, the statement is considered false. Providing a counterexample involves demonstrating specific values for m and n that do not satisfy the equation m = kn - 1, thus disproving the statement.

(c) The equation x^2 = 0 has solutions if and only if x is equal to 0.

To understand this, let's consider the quadratic equation x^2 = 0. To find its solutions, we need to determine the values of x that satisfy the equation.

If we take the square root of both sides of the equation, we get x = sqrt(0). The square root of 0 is 0, so x = 0 is a solution to the equation.

Now, let's examine the "if and only if" statement. It means that the equation x^2 = 0 has solutions only when x is equal to 0, and it has no other solutions. In other words, 0 is the only value that satisfies the equation.

We can verify this by substituting any other value for x into the equation. For example, if we substitute x = 1, we get 1^2 = 1, which does not satisfy the equation x^2 = 0.

Therefore, the equation x^2 = 0 has solutions if and only if x is equal to 0.

(d)When discussing the primality of p, we typically consider its divisibility by other numbers. A prime number has only two divisors, 1 and itself. If any other divisor exists, then p is not prime.

To determine if p is prime, we can check for divisibility by numbers less than p. If we find a divisor other than 1 and p, then p is not prime. On the other hand, if no such divisor is found, then p is considered prime.

Prime numbers play a crucial role in number theory and various mathematical applications, including cryptography and prime factorization. Their unique properties make them significant in various mathematical and computational fields.

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