Felice swims 3 times every 7 days.
How many times will she
swim in 28 days?

Answer:

actually what is this is you is this a geometry, trigonometry I don't know what to call

The exponent in Sam’s product is -5.

What does a math exponent mean?

Let us first multiply 500 with 3. 625×10-8

3. 625×10-8  × 500 = 1812.5 × 10⁻⁸

Then Sam has reported this answer in scientific notation

The format for writing a number in scientific notation is

(first digit of the number) followed by (the decimal point) and then (all the rest of the digits of the number), times (10 to an appropriate power).

In 1812.5 × 10⁻⁸  we move the decimal 3 times to left side

Since the decimal is moved left side, we multiply by 10³

1812.5 × 10⁻⁸ = 1812.5 × 10⁻⁸ × 10³

1812.5 × 10⁻⁸  = 1812.5 × 10⁻⁵

Exponent is a quantity representing the power to which a given number or expression is to be raised

1812.5 × 10⁻⁵ exponent is -5

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The third measurement of the park is approximately 624.42 ft.

To find the third measurement of the park, we need to use the properties of a right triangle and apply the Pythagorean theorem.

Let's label the measurements as follows:

The length of the department store building = 610 ft (let's call it A)

The length of the bank = 140 ft (let's call it B)

The third measurement of the park (the unknown side) = C

According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Using the Pythagorean theorem, we have:

A^2 + B^2 = C^2

Substituting the known values:

610^2 + 140^2 = C^2

370,810 + 19,600 = C^2

390,410 = C^2

To find C, we take the square root of both sides:

C = √390,410

C ≈ 624.42 ft

As a result, the park's third measurement is roughly 624.42 feet.

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The measures in the circle given in the image above are calculated as:

1. m<PSQ = 130°;   2. m<AQS = 30°; 3. m(QR) = 100°; 4. m(PS) = 110°; 5. (RS) = 70°.

In order to find the measures in the circle shown, recall that according to the inscribed angle theorem, the measure of intercepted arc is equal to the central angle, but is twice the measure of the inscribed angle.

1. m<PSQ = m<PAQ

Substitute:

m<PSQ = 130°

2. Find m<PBQ:

m<PBQ = 1/2(m(PQ) + m(RS)) [based on the angles of intersecting chords theorem]

Substitute:

m<PBQ = 1/2(130 + 2(35))

m<PBQ = 100°

m<AQS = 180 - [m<BAQ + m<PBQ]

Substitute:

m<AQS = 180 - [(180 - 130) + 100]

m<AQS = 30°

3. m(QR) = m<QAR

Substitute:

m(QR) = 100°

4. m(PS) = 180 - m(RS)

Substitute:

m(PS) = 180 - 2(35)

m(PS) = 110°

5. m(RS) = 2(35)

m(RS) = 70°

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Step-by-step explanation:

• no solution:

3x+9+4x+x = 8x + 9

• one solution:

3x+9+4x+x = 7x + 11

• infinitely many solutions:

3x+9+4x+x = 8x + 11

The 99 % confidence interval for u, given the lifetimes for the brand following a normal distribution, would be C. 48.39 to 51.61.

To construct a 99% confidence interval for the population mean (µ), we can use the formula for a confidence interval, which is:

Confidence Interval = Sample mean ± (Z-value * (Standard deviation / √(n)))

The Z-value for a 99% confidence level is approximately 2.58 according to the standard normal distribution table.

The confidence interval is therefore:

Confidence Interval = 50 ± (2.58 * (5 / √(64)))

Confidence Interval = 50 ± (2.58 * (5 / 8))

Confidence Interval = 50 ± 1.6125

Lower limit:

= 50 - 1.6125

= 48.39

Upper limit:

= 50 + 1.6125

= 51.61

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Answer:

A), C), E)

Step-by-step explanation:

The point (-12/13, 5/13) lies on the unit circle and represents a specific angle with corresponding cosine and sine values.  x² + y² = 1

To show that the point (-12/13, 5/13) is on the unit circle, we need to demonstrate that it satisfies the equation of the unit circle, which is x² + y² = 1.

Let's substitute the given values into the equation and see if it holds: (-12/13)² + (5/13)² = 1 Simplifying, we have:  144/169 + 25/169 = 1 Combining the fractions, we get: 169/169 = 1

This confirms that the point (-12/13, 5/13) satisfies the equation x² + y² = 1, which is the equation of the unit circle. The unit circle is a circle with a radius of 1 centered at the origin (0,0) in the Cartesian coordinate system.

The equation x² + y² = 1 represents all the points on the unit circle. By substituting the x and y coordinates of the given point into the equation and obtaining a result of 1, we have shown that the point lies on the unit circle.

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Step-by-step explanation:

Line AB = sqrt18 = 4.24

Line BC = sqrt10 = 3.16

Line AC = 4

Since the triangle cannot be isosceles or equilateral, the best option here is scalene.

Answer:

Line AB = 4.24

BC = 3.16

AC = 4

So ABC is scalene.

If the values do not differ by more than 0.01 points apart, the values are very precise.

The term precision refers to the fact that the values are quite close together. The values that are precise are not scattered and do not contain outliers. Precision is important when we are handling replicate measurements.

As a matter of fact, the closer the values in the measurement are to each other, the better the precision. Hence, if the values do not differ by more than 0.01 points apart, the values are very precise.

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Hank: 1.3 pounds at a rate of 0.75 pounds per minute

Tom: 2.5 pounds at a rate of 0.5 pounds per minute

rate is given by

r = p / t

where p is the number of pounds picked during a fixed time

The number of berries picked by Hank during a certain time is given by the following equation

For Tom, the equation is the following:

Now, we need to find a time t when T and H are the same

We now just need to solve for t

Let's find t step by step

Which is the same as t=4.8

Area of the scale drawing is 10 square inches. Area of the actual deck would be 160 square feet.

Area of the actual deck would be 16 times the area of the scale drawing.

Area of a two dimensional shape is the total region which is bounded by the object's shape.

Given scale drawing can be made into two squares.

One with a side length of 1 inch and other with side length of 3 inches.

Area of a square with side length 'a' = a²

Area of the given scale drawing = (1 inch)² + (3 inches)²

                                                     = 1 inch² + 9 inches²

                                                     = 10 inches²

If the scale is 1 inch = 4 feet,

Area of the actual deck = (1 × 4 feet)² + (3 × 4 feet)²

                                       = 4² [(1 feet)² + (3 feet)²]

                                       = 4² (10)

                                       = 160 feet²

Area of the actual deck = 160 feet²

                                        = 16 (Area of the scale drawing)

If the scale is 1 inch = k feet,

Area of the actual deck = k² ( Area of scale drawing)

                                        = 10 k² square feet

Hence the area of the actual deck would be 10k² if the scale is 1 inch = k feet.

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Answer: 7/6

Step-by-step explanation:

\(x^{2/3}x^{1/2}=x^{\frac{2}{3}+\frac{1}{2}}=x^{7/6}\)

Remember that

the area of the circle is

A=pi*(r^2)

we have

r=9.2/2=4.6 m ------> the radius is half the diameter

substitute

A=pi*(4.6^2)

using a calculator

(Note: the value of pi is the value that appear in the calculator)

Answer:

2., an irrational number

Step-by-step explanation:

Answer:

5.55 points

Step-by-step explanation:

25% reduction so its 75% of the original value

75% of 7.4 is 5.55

As we know that angle of semi circle is 180°.

Here,

FLG = 40°

GLH = ?

HLJ = 60°

FLG + GLH + HLG = 180°

40° + GLH + 60° = 180°

GLH + 100° = 180°

GLH = 180° - 100°

GLH = 80°

Now,

FLH = 40° + 80° = 120°

\( \sf \: Length \: of \: an \: arc \: of \: GHF = \dfrac{ \theta}{360} \times 2 \pi \: r\)

\( = \dfrac {120}{360} \times 2 \times \dfrac{22}{7} \times r\)

\( = \frac{1}{3} \times \frac{44}{7} \times r\)

\( = \frac{44}{21} \times r\)

\( = 2.09r\)

The percent sales tax of the purchase is 3 %.

A sales tax is a consumption tax imposed by the government on the sale of goods and services.

She went shopping for a new pair of sneakers.

The listed price of the pair of sneakers was $43, but the price with tax came to $44.29.

Therefore, the percent sales tax can be found as follows:

sales tax = 44.29 - 43

sales tax = $1.29

Therefore,

percent sale tax = sale tax / cost with tax × 100

percent sale tax =  1.29 / 43 × 100

percent sale tax = 129 / 43

Therefore,

percent sale tax = 3%

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Answer:

10.6

Step-by-step explanation:

just divide 42.2 and 4 and you get 10.6

Answer:

10.6 lb/box

Step-by-step explanation:

42.4/4 = 40/4 + 2.4/4

10 + 0.6 = 10.6

(A) If you divide the water into n layers, the type of geometric object you will use to approximate the ith layer is cylindrical. (B) Total work done to raise the entire tank = W = ∑W_i = ∫(4 to 0) F_i * x dx. (C) Using similar triangles, the radius  of the ith layer in terms of x is  (5 - x) / 5 * 2. (D) The volume of the ith layer of the tank is pi * h * (r_i^2 - r_(i+1)^2) = pi * (1/n) * [((5 - xi) / 5 * 2)^2 - ((5 - xi-1) / 5 * 2)^2]. (E) The mass of the ith layer, m_i = density of water * volume of the ith layer= 1000 * pi * (1/n) * [((5 - xi) / 5 * 2)^2 - ((5 - xi-1) / 5 * 2)^2]. (F) The force required to raise the ith layer, F_i = m_i * g = 9.8 * 1000 * pi * (1/n) * [((5 - xi) / 5 * 2)^2 - ((5 - xi-1) / 5 * 2)^2]. (G)  The work done to raise the ith layer of the tank, W_i = F_i * d_i = F_i * xi = 9.8 * 1000 * pi * (xi / n) * [((5 - xi) / 5 * 2)^2 - ((5 - xi-1) / 5 * 2)^2]. (H) The total work done to empty the entire tank, W = ∑W_i= ∫(4 to 0) F_i * x dx= ∫(4 to 0) 9.8 * 1000 * pi * (xi / n) * [((5 - xi) / 5 * 2)^2 - ((5 - xi-1) / 5 * 2)^2] dx.

To solve this problem, we will use the following :

(A) If you divide the water into n layers, state what type of geometric object you will use to approximate the ith layer?We will use a cylindrical shell to approximate the ith layer.

(B) Draw a figure showing the ith layer and all the important values and variables required to solve this problem. The figure representing the ith layer is shown below:

The important values and variables required to solve the problem are:

Radius of the cylindrical shell = r = (5 - x) / 5 * 2

Height of the cylindrical shell = h = 1/n

Total mass of the ith layer = m_i = 1000 * pi * r^2 * h * p_i

Force required to raise the ith layer = F_i = m_i * g

Work done to raise the ith layer = W_i = F_i * d_i = F_i * x

Total work done to raise the entire tank = W = ∑W_i = ∫(4 to 0) F_i * x dx.

(C) Using similar triangles, express the radius of the ith layer in terms of x.

From the above figure, the following similar triangles can be obtained:

ABE ~ ACIandBCF ~ CDI

AE = 2, CI = 5 - x, CI/AC = BF/BCor BF = BC * CI/AC = (2 * BC * (5 - x))/5

Therefore, the radius of the cylindrical shell, r = (5 - x) / 5 * 2.

(D) Find the volume of the ith layer.

The volume of the ith layer of the tank, V_i = pi * h * (r_i^2 - r_(i+1)^2) = pi * (1/n) * [((5 - xi) / 5 * 2)^2 - ((5 - xi-1) / 5 * 2)^2].

(E) Find the mass of the ith layer.

The mass of the ith layer of the tank, m_i = density of water * volume of the ith layer= 1000 * pi * (1/n) * [((5 - xi) / 5 * 2)^2 - ((5 - xi-1) / 5 * 2)^2].

(F) Find the force required to raise the ith layer.

The force required to raise the ith layer of the tank, F_i = m_i * g = 9.8 * 1000 * pi * (1/n) * [((5 - xi) / 5 * 2)^2 - ((5 - xi-1) / 5 * 2)^2].

(G) Find the work done to raise the ith layer.

The work done to raise the ith layer of the tank, W_i = F_i * d_i = F_i * xi = 9.8 * 1000 * pi * (xi / n) * [((5 - xi) / 5 * 2)^2 - ((5 - xi-1) / 5 * 2)^2].

(H) Set up, but do not evaluate, an integral to find the total work done in emptying the entire tank.

The total work done to empty the entire tank, W = ∑W_i= ∫(4 to 0) F_i * x dx= ∫(4 to 0) 9.8 * 1000 * pi * (xi / n) * [((5 - xi) / 5 * 2)^2 - ((5 - xi-1) / 5 * 2)^2] dx.

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Answer:

The rule that explains why the two triangles are congruent is the Angle-Angle-Side (AAS) congruence theorem:

Step-by-step explanation:

According to the Vertical Angle Theorem, opposite vertical angles of two straight intersecting lines are congruent. Therefore:

From inspection of the triangles:

Therefore, triangle NHM and triangle KHJ have two congruent angles and one congruent side.  As the side is not included between the two angles, the rule that explains that the triangles are congruent is AAS.

If any two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

Using the probability, if you choose two cards out of a deck of cards, then the chances one is a red face card and the other is a black non-face card is 1/2.

In the given question,

If you choose two cards out of a deck of cards, then we have to find the chances one is a red face card and the other is a black non-face card.

As we know that in a deck having 52 cards. In which 26 are red and 26 are black.

We have to choose a red face card.

As we know that in a deck have 12 face cards. In which 6 red face cards and 6 black face cards.

So the chance of getting red face card is

P(R)=Total number of red face cards/Total number of cards

P(R)=6/52

We have to choose a black non-face card.

We know that in a deck have 6 black face cards and total black cards are 26. So the non face cards are 20.

So the chance of getting black non-face card is

P(B)=Total number of black non-face cards/Total number of cards

P(B)=20/52

Now the chances of getting one is a red face card and the other is a black non-face card is

P(R or B)=P(R)+P(B)

P(R or B)=6/52+20/52

P(R or B)=(6+20)/52

P(R or B)=26/52

P(R or B)=1/2

Hence, if you choose two cards out of a deck of cards, then the chances one is a red face card and the other is a black non-face card is 1/2.

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The population of butterflies in four regions with respect to the change in temperature is solved

Given data ,

No trend is discernible in Region A.

In Region A, there doesn't seem to be a pattern between temperature and butterfly abundance.

Exponential Trend, Region B

With temperature , the number of butterflies seems to grow dramatically.

Negative linear trend in Region C. With increasing temperature, the number of butterflies declines rather regularly.

Positive linear trend in region D. With rising temperatures, the number of butterflies rises rather steadily.

Hence , the exponential growth factor is solved

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The complete question is attached below :

The table shows the change in the population of butterflies in four regions with respect to the change in temperature.

Answer: x = 18

Step-by-step explanation:

1) 100% - 54.5% = 45.5%.

2) 45.5/100 = 0.455.

3) 0.455 * X = 8.19g.

4) x = 8.19/0.455.

5) x = 18.

The definition of SSS, SAS, and AAS congruency conditions is shown.

SSS condition:

In accordance with the SSS rule, two triangles are considered to be congruent if their corresponding three sides are equal on both triangles.

SAS condition:

The two triangles are congruent if two sides and the included angle of one triangle match those of a second triangle by two sides and the included angle.

AAS condition:

The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

Therefore, the definition of SSS, SAS, and AAS congruency conditions is shown.

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Answer:

Step-by-step explanation:

Give jamila's Mean earning = $24

let her ninth earning be x

we know that mean= (∑sumation of earnings)/number of earnings

\(24= \frac{15+20+ 10+ 12+ 20+ 16+ 18+ 25+x}{9}\)

\(24= \frac{136+x}{9} \\24*9=136+x\\216=136+x\\x=136-216\\x=80\)

Her ninth earning is $80

The amount of blood that a cylindrical tube hold will be 0.23 cubic dm.

Let r be the radius and h be the height of the cylinder. Then the volume of the cylinder will be

V = π r²h cubic units

A cylindrical tube 14.5 cm high and 4.5 cm in diameter is used to collect blood samples. Then the radius of the cylinder will be

r = d / 2

r = 4.5 / 2

Then the volume of the cylinder will be

V = π r²h

V = 3.14 (4.5 / 2)² × 14.5

V = 3.14 × 20.25 × 14.5 / 4

V = 921.98 / 4

V = 230.5 cubic cm

V = 0.23 cubic dm

The amount of blood that a cylindrical tube hold will be 0.23 cubic dm.

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's' and 't' represent free parameters that can take on any real values.

In the given system of equations:

x1 - x2 + 4x3 = -4

6x1 - 5x2 + 7x3 = -5

3x1 - 39x3 = 45

To solve this system, we can use the method of Gaussian elimination or matrix operations. Let's use Gaussian elimination:

Step 1: Write the augmented matrix for the system:

[1 -1 4 | -4]

[6 -5 7 | -5]

[3 0 -39 | 45]

Step 2: Perform row operations to transform the matrix into row-echelon form:

R2 = R2 - 6R1

R3 = R3 - 3R1

The updated matrix becomes:

[1 -1 4 | -4]

[0 1 -17 | 19]

[0 3 -51 | 57]

Step 3: Perform additional row operations to further simplify the matrix:

R3 = R3 - 3R2

The updated matrix becomes:

[1 -1 4 | -4]

[0 1 -17 | 19]

[0 0 0 | 0]

Step 4: Write the system of equations corresponding to the row-echelon form:

x1 - x2 + 4x3 = -4

x2 - 17x3 = 19

0 = 0

Step 5: Express the variables in terms of a parameter:

x1 = s

x2 = 19 + 17s

x3 = t

where s and t are parameters.

Therefore, the solution to the system is:

[x1] = [s]

[x2] = [19 + 17s]

[x3] = [t]

In the provided solution format:

[x1] = [s] []

[x2] = [19 + 17s] + s []

[x3] = [t] [__]

Here, 's' and 't' represent free parameters that can take on any real values.

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