Patricia bought


4


4 apples and


9


9 bananas for


$


12. 70


$12. 70. Jose bought


8


8 apples and


11


11 bananas for


$


17. 70


$17. 70 at the same grocery store.


What is the cost of one apple?

The absolute maximum of the function f(x,y) = y√(x-y^2)-x+3y on the domain 0≤x≤9, 0≤y≤8 is 2√2, which occurs at the point (2,2).

The absolute minimum of the function is -8, which occurs at the point (0,2).

To find the absolute maximum and minimum of the function f(x,y) = y√(x-y^2)-x+3y on the domain 0≤x≤9, 0≤y≤8, we need to evaluate the function at the critical points and at the boundary of the domain.

The critical points of the function are the points where the partial derivatives with respect to x and y are both zero. Solving these equations, we get:∂f/∂x = -1 + y/(√(x-y^2)) = 0∂f/∂y = √(x-y^2) - 1 + 3 = 0Solving these equations, we get two critical points: (0,2) and (2,2). Evaluating the function at these points, we get:f(0,2) = -8f(2,2) = 2√2Next, we need to evaluate the function at the boundary of the domain. This includes the points (0,y), (9,y), (x,0), and (x,8).

Evaluating the function at these points, we get:f(0,y) = -x+3yf(9,y) = y√(9-y^2)-6f(x,0) = -xf(x,8) = 8√(x-64/9)-x+24Taking the maximum and minimum values of the function at the critical points and on the boundary of the domain, we see that the absolute maximum of the function is 2√2, which occurs at the point (2,2), and the absolute minimum of the function is -8, which occurs at the point (0,2).

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Answer:

Step-by-step explanation:

[tex]x^{2}[/tex]=a²+b²

x²=6²+2.5²

x²=36+6.25

x²=42.25

√x=√42.25

x=6.5

Answer:

6.5

Step-by-step explanation:

6^2 + 2.5^2 = c^2

•36 + 6.25 = c^2

•42.25 = c^2

• find square root of 42.25 = 6.5

• 6.5 = C

The matrices are: C = [140, 24, 2, 11, 61]           P = [160, 4, 13, 21, 656] B = [40, 5, 1, 81, 23]

To represent the nutritional values of the chicken, potato salad, and broccoli in matrices, we can use a 1x5 matrix for each food, where each column represents a different nutritional value in the following order: calories, protein, fat, calcium, and sodium.

Therefore, we have:

C = [140 24 2 11 61]
P = [160 4 13 21 656]
B = [40 5 1 81 23]

In matrix C, the values are 140 calories, 24 grams of protein, 2 grams of fat, 11 milligrams of calcium, and 61 milligrams of sodium for a 3 ounce serving of roasted skinless chicken breast. In matrix P, the values are 160 calories, 4 grams of protein, 13 grams of fat, 21 milligrams of calcium, and 656 milligrams of sodium for one half cup of potato salad. In matrix B, the values are 40 calories, 5 grams of protein, 1 gram of fat, 81 milligrams of calcium, and 23 milligrams of sodium for one broccoli spear.

These matrices can be used to perform calculations and comparisons between the nutritional values of the different foods.

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The radius of the circle is 2mm

It is important to note that the formula that is used for calculating the circumference of a circle is expressed with the equation.

The equation is written as;

C = 2πr

Such that the parameters are;

From the information given, we have thatt;

The radius of the circle = r

The circumference = 12.56mm

Substitute the values, we have;

12. 56 = 2×3.14r

Multiply the values

r = 12. 56/6. 28

divide the values

r = 2mm

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Answer:Go to the 6 number on the bottom line.Then go up until you reach 2

Step-by-step explanation:
|      
|
|
|
|        .  
|______

Should look like that-ish

Answer:

Step-by-step explanation:

Put the point to the right 6 times and up two times

Step-by-step explanation:

[tex]6x + 26 = 16x\\ 16x - 6x = 26 \\ 10x = 26 \\ x = 2.6[/tex]

The scale factor of the similar figure is 2.

Scale factor is the ratio of the length of a new object to the original object.

To calculate the scale factor of the similar figures, we use the formula below

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

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Answer:

4.28

Step-by-step explanation:

To find what the length of AC is, we can use the tangent of angle A, which is 35°.  Here's the equation:

tan(35)=3/x

multiply both sides by x

x·tan(35)=3

divide both sides by the tangent of 35

x=4.28 (rounded to the nearest hundredth)

This means that AC=4.28

Hope this helps! :)

Given that MNPQ is a rectangle with verticles M(3, 4), N(1, -6), and P(6, -7), to find the coordinates of point Q, we can use the fact that opposite sides of a rectangle are parallel and have equal lengths.

First, let's find the vector MN and MP:

MN = N - M = (1 - 3, -6 - 4) = (-2, -10)
MP = P - M = (6 - 3, -7 - 4) = (3, -11)

Now, let's add the vector MN to point P:

Q = P + MN = (6 + (-2), -7 + (-10)) = (4, -17)

Therefore, the coordinates of point Q that make MNPQ a rectangle are Q(4, -17).


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The distance that the bees cover in feet is 10.84 feet.

The speed at which the bees travel is given in the unit inches per min but the required solution is in feet so we need to convert the unit from in/min to ft/min using the unit conversion method.

We know that

1 inch=1/12feet.

so 32 inches/min=32.5 *(1/12) feet/min.

which is roughly equal to 2.71 feet/min (rounded to two decimal places).

Now by using the speed, distance, and time formula which is:

distance=speed*time

we can calculate the distance covered by bees at the given speed and time.

Substituting the values in the equation.

distance=2.71 feet/minute * 4.0 minutes.

=10.84 feet

Therefore, the bee's distance in feet will be 10.84 feet (rounded off to 2 digits).

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The domain of the function is the set of all positive integers, since the sequence starts with the first term and continues indefinitely. Therefore, Rosita should use the domain of positive integers for her function to generate the given sequence.

An explicit function is a mathematical expression that directly relates an independent variable to a dependent variable. In the case of Rosita's function, t(n) represents the nth term in the geometric sequence and is dependent on the value of n, the term number.

The explicit function that Rosita came up with is t(n)=160(1/2)^n, which can be simplified to t(n)=80(1/2)^(n-1). This function represents the relationship between the term number and the corresponding value in the sequence.

To determine the domain of the function, we need to consider the values of n that generate the given sequence. Looking at the sequence, we can see that the first term is 80 and each subsequent term is half of the previous term. This means that the sequence is generated by multiplying 80 by (1/2) raised to a power. We can write this as:

80(1/2)^(n-1)

where n is the term number. The domain of the function is the set of all positive integers, since the sequence starts with the first term and continues indefinitely. Therefore, Rosita should use the domain of positive integers for her function to generate the given sequence.

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1)  All the solution are,

(x, y) = (√2, 2) , (- √2, 2), (√2, -2) , (- √2, -2), (√2i, 2) , (- √2i, 2), (√2i, -2) , (- √2i, -2),

2) Solutions are,

⇒ x = 3, 3, - √3 / 2, - 5

3) All the even integers which are divisible by 5 is,

⇒ 10, 20, 30, 40, 50, ....

Given that;

1) Expression is,

⇒ x² = y, and y² = 4

2) Expression is,

⇒ (x - 3)² (2x + √3) (x + 5) = 0

Now, We can simplify as;

⇒ x² = y,

⇒ x⁴ = y²

x⁴ = 4

x⁴ - 2² = 0

(x²)² - 2² = 0

(x² - 2) (x² + 2) = 0

This gives,

x² = 2

x = ± √2

x² = - 2

x = ±√2 i

Hence, We get;

y² = 4

y = ± 2

Thus, All the solution are,

(x, y) = (√2, 2) , (- √2, 2), (√2, -2) , (- √2, -2), (√2i, 2) , (- √2i, 2), (√2i, -2) , (- √2i, -2),

Since, 2) Expression is,

⇒ (x - 3)² (2x + √3) (x + 5) = 0

Simplify as;

⇒ (x - 3)² = 0

⇒ x = 3, 3

⇒ (2x + √3) = 0

⇒ x = - √3 / 2

⇒ (x + 5) = 0

⇒ x = - 5

3) All the even integers which are divisible by 5 is,

⇒ 10, 20, 30, 40, 50, ....

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The length of arc CD, given that the radius, EB = 15 cm, is 29.31 cm

First, we shall determine ∠CED. Details below:

2∠CED + 2∠BEC = 360

2∠CED + (2 × 68) = 360

2∠CED + 136 = 360

Collect like terms

2∠CED = 360 - 136

2∠CED = 224

Divide both sides by 2

∠CED = 224 / 2

∠CED = 112°

Finally, we shall determine the length of the of arc CD. Details below:

Length of arc = 2πr × (θ / 360)

Length of arc CD = (2 × 3.14 × 15) × (112 / 360)

Length of arc CD = 29.31 cm

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Complete question:

See attached photo

The amount change in her bank account during that week after withdrawals and deposit is equal to $59.

Total number of withdrawals made by Sheila = 4

Amount made at the time withdrawals using ATM = $40

Amount withdraw using check card to purchase = $156

Amount deposited using paycheck = #375

Let us calculate the total amount of money Sheila withdrew from her bank account using ATM,

4 withdrawals of $40 each

= 4 x $40

= $160

So, she withdrew $160 and made a $156 purchase, meaning she spent a total amount of,

= $160 + $156

= $316

Sheila also deposited her paycheck of $375, so the total amount of money in her account changed by is equal to,

$375 - $316 = $59

Therefore, the amount in Sheila's account increased by $59 during that week.

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The above question is incomplete, the complete question is:

During one week, Sheila made several changes to her bank account. She made four withdrawals of $40 each from an ATM. She also used her check card for a $156 purchase. Then she deposited her paycheck of $375. By how much did the amount in her bank account change during that week?

a. A customer would save $492 during the first year by switching from ElectroniSource to Intellivision. b. A customer who would save $207 in the second year. c. Intellivision's total cost of $1654.56.

Algebra is a branch of mathematics that deals with the manipulation and properties of variables, symbols, and equations. In algebra, variables represent unknown quantities, and equations represent relationships between those unknown quantities.

The fundamental operations in algebra are addition, subtraction, multiplication, and division. Algebraic equations involve variables and constants, which are combined using these operations to form algebraic expressions. These expressions can be simplified by applying algebraic rules and properties, such as the distributive property, associative property, and commutative property.

a. To calculate the savings during the first year, we need to find the total cost for each company for all three services during a year and compare them.

For ElectroniSource, the total cost for a year would be:

$42/month x 12 months = $504 for phone service

$35/month x 12 months = $420 for Internet service

$59/month x 12 months = $708 for cable TV service

Total cost for a year with ElectroniSource = $504 + $420 + $708 = $1632

For Intellivision, the flat monthly fee is $95, so the total cost for a year would be:

$95/month x 12 months = $1140

Savings during the first year = Cost with ElectroniSource - Cost with Intellivision

= $1632 - $1140

= $492

Therefore, a customer would save $492 during the first year by switching from ElectroniSource to Intellivision.

b. After the first year, Intellivision raises the rates by 25%. The new monthly fee would be:

$95 + 25% of $95 = $118.75

To calculate the savings for the second year, we need to find the total cost for each company for all three services during the second year and compare them.

For ElectroniSource, the total cost for the second year would still be:

$504 for phone service

$420 for Internet service

$708 for cable TV service

Total cost for the second year with ElectroniSource = $504 + $420 + $708 = $1632

For Intellivision, the total cost for the second year would be:

$118.75/month x 12 months = $1425

Savings during the second year = Cost with ElectroniSource - Cost with Intellivision

= $1632 - $1425

= $207

Therefore, a customer who switched from ElectroniSource to Intellivision would save $207 in the second year.

c. If Intellivision raises the rates by 16% for the third year compared to the second year, the new monthly fee would be:

$118.75 + 16% of $118.75 = $137.88

To compare the total cost for each company for the third year, we need to find the total cost for each company for all three services during the third year and compare them.

For ElectroniSource, the total cost for the third year would still be:

$504 for phone service

$420 for Internet service

$708 for cable TV service

Total cost for the third year with ElectroniSource = $504 + $420 + $708 = $1632

For Intellivision, the total cost for the third year would be:

$137.88/month x 12 months = $1654.56

Therefore, ElectroniSource is cheaper for the third year, with a total cost of $1632 compared to Intellivision's total cost of $1654.56.

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The expected value of each warranty sold is $2.47.

The expected value of each warranty sold can be calculated by subtracting the cost of the warranty from the expected value of the potential savings on replacement costs.

Let's assume that the company sells 1000 warranties. Then, the expected number of products that will fail within 2 years is:

0.5% of 1000 = 0.005 x 1000 = 5

The expected cost of replacing these products is:

5 x $500 = $2500

Therefore, the expected value of the warranty is:

($2500 - $33 x 1000) / 1000 = $2.47

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The equation has at least one solution in the interval (-1, 1).

To prove that the equation has at least one solution in the interval (-1, 1), we can use the Intermediate Value Theorem.

First, let's simplify the equation by finding a common denominator:

a(x^3+x-2) + b(x^3+2x^2-1) = 0

Now, let's define a new function f(x) = a(x^3+x-2) + b(x^3+2x^2-1). This function is continuous on the interval (-1, 1) because it is a sum of continuous functions.

Next, we will evaluate f(-1) and f(1) to see if the Intermediate Value Theorem can be applied.

f(-1) = a(-1^3-1-2) + b(-1^3+2(-1)^2-1) = -a-b < 0

f(1) = a(1^3+1-2) + b(1^3+2(1)^2-1) = a+3b > 0

Since f(-1) is negative and f(1) is positive, there must be at least one value of x in the interval (-1, 1) such that f(x) = 0, by the Intermediate Value Theorem.
To prove that the given equation has at least one solution in the interval (-1, 1), we can use the Intermediate Value Theorem (IVT). Let's define the function f(x) as follows:

f(x) = a/(x^3 + 2x^2 - 1) + b/(x^3 + x - 2)

Since a and b are positive numbers, we can examine the behavior of f(x) at the endpoints of the interval (-1, 1).

f(-1) = a/((-1)^3 + 2(-1)^2 - 1) + b/((-1)^3 + (-1) - 2)
f(-1) = a/(-1) + b/(-4) < 0

f(1) = a/(1^3 + 2(1)^2 - 1) + b/(1^3 + 1 - 2)
f(1) = a/(2) + b/(0) = a/2 > 0

Since f(-1) < 0 and f(1) > 0, by the Intermediate Value Theorem, there must be at least one point c within the interval (-1, 1) where f(c) = 0. This means that the given equation has at least one solution in the interval (-1, 1).

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Based on the hypothesis test, with a significance level of 0.05, there is no evidence to suggest that the die is loaded, as the p-value is greater than the significance level. The null hypothesis that the die is fair is failed to rejected.

To determine if the die is loaded, we need to perform a hypothesis test.

Null Hypothesis (H0) The die is fair; all outcomes are equally likely.

Alternative Hypothesis (Ha) The die is loaded, and not all outcomes are equally likely.

We will use a significance level of 0.05.

To test the hypothesis, we can use a chi-square goodness-of-fit test.

First, we need to calculate the expected frequencies for each outcome, assuming that the die is fair. Since there are six possible outcomes, each with an expected frequency of 200/6 = 33.33.

Number Observed Frequency (O) Expected Frequency (E) (O - E)² / E

1 45 33.33 3.48

2 39 33.33 0.87

3 35 33.33 0.07

4 25 33.33 1.83

5 27 33.33 0.99

6 29 33.33 0.44

The test statistic is the sum of (O-E)² / E, which is 7.68.

The degrees of freedom for this test are (number of categories - 1) = 5.

Using a chi-square distribution table or calculator, we find that the p-value associated with a test statistic of 7.68 and 5 degrees of freedom is approximately 0.177.

Since the p-value is greater than our significance level of 0.05, we fail to reject the null hypothesis. We cannot conclude that the die is loaded based on this data alone.

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An equivalent function of the given function in the form G(t) = [tex]ab^t[/tex] is G(t) = 24000[tex](0.9025)^t[/tex].

The given function for the value of a car that depreciates over time is G(t) = 24000[tex](0.95)^{2t[/tex]. To write an equivalent function of the form G(t) = [tex]ab^t[/tex], we need to rewrite the function using exponent rules.

First, we can rewrite [tex](0.95)^{2t[/tex] as [tex][(0.95)^{2}]^{t[/tex], which simplifies to [tex](0.9025)^t[/tex]. Therefore, we have:

G(t) = 24000[tex](0.9025)^t[/tex]

Next, we need to express 24000 as a product of two factors, a and b. We can choose a = 24000 and b = 0.9025, so we have:

G(t) = 24000[tex](0.9025)^t[/tex] = 24000[tex](0.9025)^t[/tex]

This function gives the value of the car at time t, where t is the number of years after the initial purchase, with a starting value of 24000 and a depreciation rate of 9.75% per year.

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The perimeter of the shaded region is approximately 85.67 cm The area of the shaded region is approximately 91.84 cm² (rounded to the nearest tenth).

To calculate the perimeter and area of the shaded region, we first need to find the radius of each circle.

The larger circle has a diameter of 21 cm, which means its radius is 10.5 cm (half of the diameter). The smaller circle has a diameter of 10 cm, so its radius is 5 cm.

To find the perimeter of the shaded region, we need to add the circumference of both circles and subtract the overlap (the length of the shared segment). The circumference of the larger circle is 2π(10.5) ≈ 65.97 cm, and the circumference of the smaller circle is 2π(5) ≈ 31.42 cm.

To find the length of the shared segment, we can use the Pythagorean theorem. The distance between the centers of the circles is 15 cm (the sum of the radii), so we can form a right triangle with legs of 10.5 cm and 5 cm. Using the Pythagorean theorem, we get:

c² = a² + b²
c² = 10.5² + 5²
c² ≈ 137.25
c ≈ 11.72

So the length of the shared segment is approximately 11.72 cm.

Therefore, the perimeter of the shaded region is approximately 65.97 + 31.42 - 11.72 = 85.67 cm (rounded to the nearest tenth).

To find the area of the shaded region, we need to subtract the area of the smaller circle from the area of the larger circle, and then subtract the area of the overlap (the area of the shared segment).

The area of the larger circle is π(10.5)² ≈ 346.36 cm², and the area of the smaller circle is π(5)² ≈ 78.54 cm².

To find the area of the shared segment, we can use the formula for the area of a sector of a circle:

A = (θ/360)πr²

where θ is the central angle of the sector. In this case, the sector has a central angle of 2cos⁻¹(5/10.5) ≈ 105.2°, so:

A = (105.2/360)π(10.5)²
A ≈ 91.84 cm²

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ANSWER:

(x+7)^2=16

Step-by-step explanation:

x^2-14x+49=16

x^2-14x+49-16=0

x^2-14x+33=0

subtract -33 on both sides

x^2-14x+33-33=-33

x^2-14x=-33

Add 49 on both sides

x^2-14x+49=-33+49

x^2-14x+49=16

x^2-7x-7x+49=16

x(x-7)-7(x-7)=16

(x-7)(x-7)=16

(x-7)^2=16

Answer:

22.69 ~ = 23 feet

Step-by-step explanation:

cos 19 = adj/24

24cos 18 = adj

adj = 22.69~= 23

Answer:

[tex]x&=\dfrac{1}{2}\pi +2\pi n,\;\; \dfrac{3}{2}\pi + 2 \pi n[/tex]

Step-by-step explanation:

Given equation:

[tex]\sin(2x)\sin(x)+\cos(x)=0[/tex]

Rewrite sin(2x) using the trigonometric identity sin(2x) = 2sin(x)cos(x):

[tex]\implies 2\sin(x)\cos(x)\sin(x)+\cos(x)=0[/tex]

[tex]\implies 2\sin^2(x)\cos(x)+\cos(x)=0[/tex]

Factor out cos(x):

[tex]\implies \cos(x)\left[2\sin^2(x)+1\right]=0[/tex]

Applying the zero-product property:

[tex]\textsf{Equation 1:}\quad\cos(x)=0[/tex]

[tex]\textsf{Equation 2:}\quad2\sin^2(x)+1=0[/tex]

Solve each part separately.

[tex]\underline{\sf Equation \; 1}[/tex]

[tex]\begin{aligned}\cos(x)&=0\\x&=\arccos(0)\\x&=\dfrac{1}{2}\pi +2\pi n,\;\; \dfrac{3}{2}\pi + 2 \pi n\end{aligned}[/tex]

[tex]\underline{\sf Equation \; 2}[/tex]

[tex]\begin{aligned}2\sin^2(x)+1&=0\\\sin^2(x)&=-\dfrac{1}{2}\;\;\;\;\;\;\leftarrow\;\textsf{No solution}\end{aligned}[/tex]

Therefore, the solutions of the equation in radians are:

[tex]\boxed{x&=\dfrac{1}{2}\pi +2\pi n,\;\; \dfrac{3}{2}\pi + 2 \pi n}[/tex]

The volume of the cones are;

1. 84. 78 in³

2.  564. 15 ft³

3.  4710 yd³

The formula for calculating the volume of a cone is expressed as;

V = 1/3 πr²h

Given that;

From the information given, we have;

1. Volume = 1/3 × 3.14 × 3² × 9

Multiply the values and find the square

Volume = 254. 34/3

divide the values

Volume = 84. 78 in³

2. Volume = 1/3 × 3.14 × 7² × 11

Multiply the values

Volume = 1692. 46/3

Volume = 564. 15 ft³

3. Volume = 1/3 × 3.14 × 15² × 20

Multiply the values

Volume = 4710 yd³

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The maximum height of Anna's golf ball is 6.25 feet.

To find the maximum height of Anna's golf ball, we need to determine the vertex of the parabolic equation y = x - 0.04x^2. The x-coordinate of the vertex can be found using the formula:

x = -b / (2a)

In this case, the coefficients a and b are:
a = -0.04
b = 1

Substituting the values into the formula:

x = -1 / (2 * -0.04)
x = -1 / (-0.08)
x = 12.5

Now, we need to find the y-coordinate of the vertex by plugging the x-coordinate back into the equation:

y = 12.5 - 0.04(12.5)^2

y = 12.5 - 0.04(156.25)

y = 12.5 - 6.25

y = 6.25

So, the maximum height of Anna's golf ball is 6.25 feet.

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Answer: The transformation is up one and to the left 5

(-5, 1)

Step-by-step explanation:

Please Give brainliest, have a great night!

Answer:   h(x) = g(x+5)+1

Step-by-step explanation:

h(x) = g(x+5)+1

You went 5 in the negative direction x direction; take the opposite sign

Also went up 1 in the y direction so add 1 to equation