look at the attached picture to see want this post is asking for.
U dont have to sketch

1. f(x) = x^2 + 6x +2

2. f(x) = 2 - 5x= 2x^2

3. f(x) = -0.25x^2 + 8x - 2

4. f(x) = 4x^2 + 3x -5

Based on Pythagorean's theorem, the lengths of the sides of △OPR are:

In Mathematics and Geometry, a perpendicular bisector bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

Since line segment OS bisects line segment PQ, we have the following:

x = QR = 35 units.

y = z + 25

By applying Pythagorean's theorem, we have the following:

x² + z² = y²

(z + 25)² = 35² + z²

z² + 50z + 625 = 1,225 + z²

50z = 1,225 - 625

50z = 600

z = 600/50

z = 30 units.

y = z + 25

y = 30 + 25

y = 55 units.

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Complete Question:

O is the centre of the circle. x, y, and z indicate the lengths of the sides of △OPR. Find with reasons the values of the following:

1.1.1   x

1.1.2  z

1.1.3  y

The 95% confidence interval for the proportion of people who prefer Candidate A is  0.8 ± 0.080.

Confidence Interval = Sample Proportion ± Margin of Error

We first determine the values for each term:

Sample Proportion = Number  / Total sample size

Sample Proportion = 68/85

Sample Proportion  = 0.8

Standard Error = √((Sample Proportion  * (1 -Sample Proportion )) / n)

n =  sample size

Standard Error = √((0.8 * (1 - 0.8)) / 85)

Standard Error = 0.041

We then calculate the Margin of Error = Critical Value * Standard Error Margin of Error = 1.96 * 0.041

Margin of Error = 0.080

We substitute all these values and calculate for :
Confidence Interval = Sample Proportion ± Margin of Error

Confidence Interval = 0.8 ± 0.080

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The value of the constants a and b is 2 and -32 respectively.

The complete factorization of the polynomial is (x - 3)(x + 5) (2x - 1).

The value of the constants is calculated as follows;

P(r) = ax³ + 3x² + bx + 15

If x - 1 is factor with a remainder of -12, then x = 1

P(1) = a1³  +  3(1²) + b(1) + 15 = -12

a + 3 + b + 15 = -12

a + b = -30

b = -30 - a

also, if x - 2 is a factor with a remainder of -21, then x = 2;

P(2) = a(2)³  +  3(2²) + b(2) + 15 = -21

8a + 12 + 2b + 15 = -21

8a + 2b = -48

4a + b = - 24

Substitute the value of b into the equation;

4a - 30 - a = - 24

3a = 6

a = 2

b = -30 - a

b = -30 - 2

b = -32

The quadratic equation will become;

P(r) = 2x³ + 3x² -32x + 15

We will factorize the equation as follows;

x - 3 is a factor;

           2x²  + 9x - 5

           ----------------------------------

x - 3 √ (2x³ + 3x² -32x + 15)

          - (2x³ - 6x²)

          ----------------------------------

                    9x² - 32x + 15

                  - (9x² - 27x )

                ----------------------------

                             -5x + 15

                           - ( -5x + 15)

                      -----------------------------

                                     0

We will factorize  2x²  + 9x - 5

= 2x² - x + 10x - 5

= x(2x - 1) + 5(2x - 1)

= (x + 5)(2x - 1)

The complete factor = (x - 3)(x + 5) (2x - 1)

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first, you distribute, so

4a ([tex]a^{2}[/tex]+7a+4)

[tex]4a^{3}[/tex]+28[tex]a^{2}[/tex]+16a

and that's your answer! :)

thanks in advance for brainliest!!

4a(a^2+7a+4) can be simplified by multiplying 4a to each term inside the parenthesis:

4a(a^2+7a+4) = 4a * a^2 + 4a * 7a + 4a * 4

This gives us:

4a^3 + 28a^2 + 16a

Therefore, 4a(a^2+7a+4) simplifies to 4a^3 + 28a^2 + 16a.

Answer:

Step-by-step explanation:

The total value of his quarters is Q x $0.25. Therefore, the combined value of his coins is:

$1.20 + Q x $0.25 = $4.75 - $3.55

Simplifying the equation, we get:

Q x $0.25 = $1.20 + $1.20

Q x $0.25 = $2.40

Q = $2.40 / $0.25

Q = 9.6

Since Q must be a whole number, the minimum number of quarters that Fabian could have is 10. (If he had only 9 quarters, the combined value of his coins would be $1.20 + $2.25 = $3.45, which is less than the required minimum of $4.75.)

Step-by-step explanation:

.94x  = x-1

.06x = 1

x = 16 2/3     which is not a whole number so there must be at LEAST 17 people in class

   then if one is a boy   there are 16 girls    16/17 = 94.11 % girls   with one boy

The type of analysis described in the statement is ratio analysis.

Ratio analysis is a tool used to evaluate the financial performance of a company by comparing different financial ratios over time or between companies. It involves calculating different ratios such as liquidity ratios, profitability ratios, and solvency ratios and comparing them across different periods to identify trends or patterns in the data. The ratio analysis formula mentioned in the statement is used to calculate the percentage change in a ratio between two periods, with the base period amount serving as the denominator.

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The formula A = πrl represents the curved surface area of a cone, where r is the radius of the base of the cone and l is the slant height.

The curved surface area of a cone is the area of the lateral or side surface of the cone. It is called curved because the surface of the cone is not flat but rather curved, like the surface of a curved cylinder. To derive this formula, we can first imagine a cone with a base that has a circumference of 2πr, where r is the radius of the base. If we cut along a generator line of the cone, we can then unroll the curved surface of the cone to form a sector of a circle with radius l and central angle 2π. The area of this sector is πl^2, which represents the total area of the curved surface of the cone. We can simplify this formula to A = πrl by substituting the value of l with the Pythagorean theorem, l^2 = r^2 + h^2, where h is the height of the cone.

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a) the distance in picometers is 135 pm. b) the distance in picometers is 135 pm. c) The answer is 7.0 × 10^4 atoms. d) The volume of a single gold atom is 9.15 × 10^(-24) cm^3.

Part A:

1.35 Å = 0.135 nm (since 1 Å = 0.1 nm)

Therefore, the distance in nanometers is 0.135 nm.

Part B:

1.35 Å = 135 pm (since 1 Å = 100 pm)

Therefore, the distance in picometers is 135 pm.

Part C:

The length of one gold atom is 1.35 Å = 1.35 × 10^(-10) m.

The number of atoms required to span a distance of 9.5 mm = (9.5 × 10^(-3) m) / (1.35 × 10^(-10) m) = 70,370 atoms.

Rounding to two significant figures, the answer is 7.0 × 10^4 atoms.

Part D:

Assuming the gold atom is a sphere, its volume can be calculated as:

V = (4/3)πr^3, where r is the radius of the atom.

Substituting the value of the radius (1.35 Å = 1.35 × 10^(-10) m) gives:

V = (4/3)π(1.35 × 10^(-10))^3 = 9.15 × 10^(-30) m^3.

Expressing this in cubic centimeters gives:

V = 9.15 × 10^(-30) × 10^6 = 9.15 × 10^(-24) cm^3.

Therefore, the volume of a single gold atom is 9.15 × 10^(-24) cm^3.

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Formula Used:-

[tex] \qquad \hookrightarrow{ \underline{ \overline{ \boxed{ \sf{Surface \: Area =3\pi {r}^{2} }}}}}\\[/tex]

[tex] \sf \longrightarrow \: Surface \: Area =3\pi {r}^{2} \: ) \\ [/tex]

[tex]\sf \longrightarrow \: Surface \: Area =3 \times \frac{22}{7} \times {r}^{2} \: \\[/tex]

[tex]\sf \longrightarrow \: Surface \: Area =3 \times \frac{22}{7} \times {11}^{2} \: \\[/tex]

[tex]\sf \longrightarrow \: Surface \: Area =3 \times \frac{22}{7} \times 11 \times 11 \: \\[/tex]

[tex]\sf \longrightarrow \: Surface \: Area = \frac{3 \times 22 \times 11 \times 11}{7} \: \\[/tex]

[tex]\sf \longrightarrow \: Surface \: Area = \frac{66 \times 11 \times 11}{7} \: \\[/tex]

[tex]\sf \longrightarrow \: Surface \: Area = \frac{66 \times 121}{7} \: \\[/tex]

[tex]\sf \longrightarrow \: Surface \: Area = \frac{7986}{7} \: \\[/tex]

[tex]\sf \longrightarrow \: Surface \: Area = 1140.8 \: {ft}^{2} \: \\[/tex]

______________________________________________

Therefore, Surface Area of Hemisphere is 1140.8 ft²

Answer:

Step-by-step explanation:

We know that,

[tex]\large {\boxed {\boxed{\bf\leadsto \: surface \: area \: of \: hemisphere \: = 3\pi {r}^{2} }}}[/tex]

Here,

Now

[tex]\large \sf\leadsto3 \times \frac{22}{7} \times 11 {}^{2} [/tex]

[tex]\large \sf\leadsto3 \times \frac{22}{7} \times 121[/tex]

[tex]\large \sf\leadsto \: \frac{66}{7} \times 121[/tex]

[tex]\large \sf\leadsto \frac{7986}{7} [/tex]

[tex] \boxed{\large \bf\leadsto1140.8 \: {ft}^{2} }[/tex]

By using Algebraic methods It will take 5 seconds for the rock to hit the ground when dropped from a building that is 64 feet tall, given the equation y = -16t^2 + 400.

The equation is y = -16t^2 + 400, where y represents the height of the rock in feet and t represents the time in seconds.
To find out how many seconds it will take for the rock to hit the ground, we need to set the equation equal to zero because the ground is at a height of zero.
0 = -16t^2 + 400
Now, we can solve for t using  Algebraic methods.
First, we can subtract 400 from both sides of the equation:
-400 = -16t^2
Next, we can divide both sides by -16:
25 = t^2
Finally, we can take the square root of both sides:
t = ±5
Since we can't have negative time, we know that it will take 5 seconds for the rock to hit the ground.
So, to summarize, it will take 5 seconds for the rock to hit the ground when dropped from a building that is 64 feet tall, given the equation y = -16t^2 + 400.

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The equation of the red graph, g(x) is g(x) = (x + 3)² - 4

From the question, we have the following parameters that can be used in our computation:

The functions f(x) and g(x)

In the graph, we can see that

This means that

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

Recall that

f(x) = x²

This means that

g(x) = (x + 3)² - 4

This means that the equation of the red graph is g(x) = (x + 3)² - 4

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The volume of the box decreases as the cutout length increases over the interval (0, 3.5/2) and increases over the interval (3.5/2, infinity).

Let the dimensions of the rectangular box be x, y, and z. The volume of the box is given by V = xyz. Suppose that the cutout length is along the x-axis, and let it be denoted by w. Then, we have:

V = (x - w)yz

Taking the derivative of V with respect to w, we get:

dV/dw = -yz

The volume of the box will decrease as the cutout length increases if dV/dw < 0, and it will increase if dV/dw > 0. Since y and z are positive, dV/dw will be negative if w is less than x/2 and positive if w is greater than x/2. Therefore, the volume of the box decreases as the cutout length increases over the interval (0, x/2) and increases over the interval (x/2, infinity).

In our case, the largest possible cutout length is 3.5 inches, so the interval over which the volume of the box decreases as the cutout length gets larger is (0, 3.5/2), which is (0, 1.75). The interval over which the volume of the box increases is (3.5/2, infinity), which is (1.75, infinity).

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Hello !

c = the cost

n boxes = 66,12n

c = 66,12n

Answer:

Step-by-step explanation:

The formula for this is:

V = (1/2) x b x h x l

b= base

h=height

l=length

V= (1/2) x 4.2 x 2.8 x 8

so...I think the volume could be 47.04m^3?

PRO TIP: If you want to solve anything with volume, just write down every single formula they have for volume or area. It is good to memorize formulas like that.

The volume of the triangular prism with a height of 2.8, width of 4.2, and a length of 8 is 46.96 cubic unit.

The base area of the triangular cross-section must be multiplied by the prism's height to determine its volume. The triangle cross-section in this instance has a base of 4.2 and a height of 8.

The following is the formula to determine a triangle's area:

(Base * Height) / 2 = Area

When the values are plugged in, we get:

Base = 4.2

Size = 8

Area = (4.2 * 8) / 2 = 33.6 / 2 = 16.8

Next, increase the prism's base area by its height:

Volume = Base Area * Height = 16.8*2.8 = 46.96

The triangular prism therefore has a 46.96 cubic unit volume.

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The volume of the composite shaped solid is V = 26,133.33 cm³

Given data ,

To calculate the volume of the composite solid consisting of a cube and a square-based pyramid

Volume of a cube = (edge length)³

V ( cube ) = ( 28 )³

V ( cube ) = 21,952 cm³

Now , The volume of a pyramid is given by the formula:

Volume of a pyramid = (base area * height) / 3

Base area = ( 28 )²

Base area = 784 cm²

Now , V ( pyramid ) = ( 784 x 16 ) / 3

V ( pyramid ) = 4,181.33 cm³

So , volume of composite solid = 21,952 cm³ + 4,181.33 cm³

V = 26,133.33 cm³

Hence , the volume is V = 26,133.33 cm³

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Answer: t=1

Final Answer=$1,020

t=1/2

Final Answer=$1,009.95

Step-by-step explanation: This is correct

its cammy, im telling that your cheating (and i definitely wasnt looking up this same question)

The area of the figure given above which is a trapezium would be = 384 in². That is option D.

To calculate the area of a trapezium, the formula that should be used is given below:

Area of cylinder = 1/2 (a+b) h

where;

a = 24 in

b = 16 in

h = 19.2 in

Area of cylinder = 1/2× (24+16) × 19.2

= 20×19.2

= 384 in²

Therefore the area of the given shape above which is a cylinder would be = 384 in^2

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We can use the fact that as x gets closer and closer to 0, the expression (1 + x)^1/x gets closer and closer to a certain value. The value of the limit to five decimal places is: 2.71828

One way to estimate this value is to use a calculator or computer program to evaluate the expression for smaller and smaller values of x, until we get a sense of what the limit might be. For example, we can plug in x = 0.001, 0.0001, 0.00001, etc., and see that the expression appears to be approaching a value of approximately 2.71828.

This value is actually a well-known mathematical constant called "e", which is approximately equal to 2.71828. Therefore, we can estimate the value of the limit lim (1 + x)^1/x to five decimal places as e, or approximately 2.71828.

To estimate the value of the limit lim (1 + x)^(1/x) as x approaches 0, we can use the fact that this limit is equal to the mathematical constant e.

lim (1 + x)^(1/x) as x -> 0 = e

e is approximately equal to 2.71828.

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The simplification of the given terms is 14.25 or 114/8

A numerical expression is a piece of algebraic information stated in the form of numbers and variables that are unknown.

We are given that 6 times 2 wholes 3/8

Let the number be x

So,6 times 2 wholes 3/8 means;

x = 6 x 2 3/8

x = 6 x 19/8

x = 14.25 or 114/8

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In the group of numbers given above, the largest and the smallest number in each group is given below respectively:

a.) -1 and -21

b.) -2 and -45

c.) 7 and -4

d.) -5 and -19

A number line is defined as the representation of numbers in the order of negative and positive numbers with zero at the center of the structure.

In a number line, the figures that are at the right of zero are the positive and larger numbers while the numbers that are on the left of zero are the negative numbers and are smaller numbers.

Therefore, -1 is greater than -2 which is in turn greater than -3.

Therefore the largest and smallest numbers of each number group respectively include the following

a.) -1 and -21

b.) -2 and -45

c.) 7 and -4

d.) -5 and -19

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There are 1234 t shirts that need to be shipped. To ship 1234 t-shirts, a total of 39 boxes are required, as each box can hold 32 t-shirts.

To calculate the number of boxes required to ship 1234 t-shirts, we need to divide the total number of t-shirts by the number of t-shirts that can fit in one box. In this case, as each box can fit 32 t-shirts, we need to divide 1234 by 32.

Using long division, we can find that 32 goes into 1234, 38 times with a remainder of 10. However, we still have 10 t-shirts that need to be shipped, which means we need an additional box to fit them. Therefore, the total number of boxes needed to ship 1234 t-shirts is 39 (38 boxes to fit 1216 t-shirts and 1 additional box to fit the remaining 10 t-shirts).

It's always important to ensure that all the items fit comfortably in the boxes without any damage or risk of items falling out. In this case, we can also use this information to plan and optimize the shipping process by arranging the boxes according to the available storage and transportation capacity.

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Answer:

B

Step-by-step explanation:

203.95 is equal to 4 of the tickets plus 11.95

You can write this as

203.95=4(price of ticket)+11.95

4(price of ticket)=192

Divide by 4

The price of a ticket is 48.

The equation would be 11.95+48t because its 48 times the amount of ticket plus the service fee.

Answer:

The age of this parrot is 16 years old, and this parrot knows 68 words.

The weight of the melted ice cream would be the same as the weight of the original ice cream, which is 5 ounces.

a quantity or thing weighing a fixed and usually specified amount. : a heavy object (such as a metal ball) thrown, put, or lifted as an athletic exercise or contest. 3. : a unit of weight or mass see Metric System Table.

When the ice cream melts, it undergoes a change in state from solid to liquid, but the total mass or weight remains unchanged. Therefore, the weight of the melted ice cream is still 5 ounces.

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The given statement is false.

In a two-tailed hypothesis test for a population mean, where the population standard deviation is known, the critical values are the values that divide the alpha (significance level) into two equal-tailed regions.

For a 1% level of significance (alpha = 0.01), a two-tailed test allocates half of the alpha to each tail of the distribution. In this case, each tail will have an area of 0.01/2 = 0.005.

The critical values are determined by the standard normal distribution (z-distribution) or by the t-distribution (if the sample size is small and the population standard deviation is unknown). These critical values represent the number of standard deviations away from the mean that correspond to the desired level of significance.

The specific critical values will depend on the sample size, distribution type (z or t), and the desired level of significance. To obtain the critical values, one would consult a standard normal distribution table or a t-distribution table, depending on the case.

In summary, the critical values in a two-tailed hypothesis test do not necessarily divide the area under the standard normal curve into a middle 0.98 area and two outside areas of 0.01. The allocation of the alpha (significance level) is determined based on the desired level of significance, and the critical values are obtained from the appropriate distribution table.

Therefore, the given statement is false

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Levi placed 10 weights on the scale, each weighing 0.7 grams. The total weight of the weights is 7 grams. Therefore, the scale will read 7 grams.

Levi placed 10 weights on the scale, and each weight weighed 0.7 grams. To find the total weight, we need to multiply the weight of one weight by the number of weights. Therefore, the total weight of the weights is 0.7 x 10 = 7 grams. This means that the scale will read 7 grams.

The principle behind this calculation is the law of conservation of mass. This law states that the total mass of a closed system remains constant, regardless of any changes that take place within the system. In this case, the system is the scale and the weights. Since the scale is a closed system, the total mass of the weights placed on it must be equal to the reading on the scale.

Therefore, when Levi placed 10 weights on the scale, the total weight of the weights is 7 grams, and the scale will read 7 grams. This calculation can be used to determine the weight of any number of objects placed on a scale, as long as the weight of one object and the number of objects are known.

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The only True statement is B: If −2/5r = −20, then r = −50

We can solve each equation to determine which statement is true.

A. If 4/3h = 12, then h = 16.

To solve for h, we can multiply both sides of the equation by 3/4:

4/3h * 3/4 = 12 * 3/4

h = 9

Therefore, statement A is false.

B. If −2/5r = −20, then r = −50.

To solve for r, we can multiply both sides of the equation by -5/2:

-2/5r * -5/2 = -20 * -5/2

r = 50

Therefore, statement B is true.

C. If 1/2 = −3/7q, then q = −116.

To solve for q, we can multiply both sides of the equation by -7/3:

1/2 * -7/3 = -3/7q * -7/3

q = 21/3 = 7

Therefore, statement C is false.

D. If 3/8 = 24c, then c = 9.

To solve for c, we can divide both sides of the equation by 24 * 8/3:

3/8 * 3/24 * 8/3 = 24c * 3/24 * 8/3

c = 1/3 * 8

c = 8/3

Therefore, statement D is false.

Therefore, the only true statement is B: If −2/5r = −20, then r = −50.

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To divide (a-3/7) by (3-a/21), we need to multiply the numerator by the reciprocal of the denominator.

Reciprocal of (3-a/21) is (21/(3-a))

So,

(a-3/7) / (3-a/21) = (a-3/7) * (21/(3-a))

Now, we can simplify by canceling out common factors between the numerator and denominator.

(a-3/7) * (21/(3-a)) = (3-a)(a-3)/(7*21)

= -(a^2 - 6a + 9)/147

= -(a-3)^2/147

Therefore, the quotient is -(a-3)^2/147.