Gregory runs a 100-meter race. 5 seconds after the race started Gregory is 30 meters from the starting line and reaches his max speed; he runs at this max speed for the rest of the race. Gregory notices that he is 62 meters from the starting line 9 seconds after the race started.

What is Gregory's max speed?

Suppose Gregory runs for an additional
z
seconds after reaching his max speed...

How far will Gregory travel during those additional
z
seconds?
What is Gregory's distance from the starting line
5
+
z
seconds after the race started?
What is Gregory's distance from the starting line
x
seconds after the race started (provided
x
≥
5
)?

area of square 1 is 28 square units and its side length is[tex]$2\sqrt{7}$[/tex] units.

Let the side length of square 1 be x units. Then the areas of squares 1, 2, and 3 are [tex]$x^2$[/tex], 64, and 36 square units, respectively.

Since square 2 has an area of $64$ square units, its side length is [tex]$\sqrt{64}=8$[/tex] units. Similarly, square 3 has a side length of[tex]$\sqrt{36}=6$[/tex]units.

We can now set up an equation based on the fact that the sum of the areas of squares 1 and 3 is equal to the area of square 2:

[tex]$$x^2+36=64$$[/tex]

Solving for x, we get:

[tex]$$x^2=28$$[/tex]

Therefore, the area of square 1 is [tex]$x^2=28$[/tex] square units, and its side length is [tex]$\sqrt{28}=2\sqrt{7}$[/tex] units.

In summary, the area of square 1 is 28 square units and its side length is[tex]$2\sqrt{7}$[/tex] units.

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Answer:

Step-by-step explanation:

First, let's simplify the equation:

(x – 3)² + 9 = 0

(x – 3)² = -9

Now we can apply the square root principle:

x – 3 = ±√(-9)

x – 3 = ±3i

Solving for x:

x = 3 ± 3i

Therefore, the answer is (a) x = 3 + 3i, 3 – 3i.

Answer:

71%

Step-by-step explanation:

We know

Tyler went to the gym on 22 of the last 31 days.

Which of the following is closest to the percentage of days that Tyler went to the gym?

We take

22 divided by 31, times 100 = 71%

So, the answer is 71%

The function representing the number of bacteria present each day is f(t) = 2032[tex](0.85)^{t}[/tex].

Both the set X and the set Y are referred to as the function's domain and codomain, respectively.

Beginning in 2032, there will be a 15% daily decline in the number of microorganisms.

a function that displays the daily average amount of microorganisms.

f(x) = 2032[tex](1 - .15)^{t}[/tex]

f(x) = 2032[tex](0.85)^{t}[/tex]

Therefore f(t) = 2032[tex]0.85^{t}[/tex] is the correct answer.

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A machine must produce a bearing that is within 0.02 inches of the correct diameter 4.1 inches. By writing this statement using absolute value notation is:

| x - 4.1 | ≤ 0.02

This notation expresses the requirement that the diameter of the bearing, represented by x, must be within 0.02 inches of the correct diameter of 4.1 inches. The absolute value of the difference between x and 4.1 must be less than or equal to 0.02 for the bearing to meet the specification.

The absolute value function is used to ensure that the difference between x and 4.1 is always positive, regardless of whether x is greater than or less than 4.1. This is important because the requirement is concerned with the magnitude of the difference, rather than its sign. If the absolute value of the difference is less than or equal to 0.02, then the diameter of the bearing is considered to be within the required tolerance.

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Measure of angle G is 62.5°.

For a regular polygon of any number of sides, the sum of its exterior angle is 360° (full angle).

In triangle EFG,

Measure of angle E = 55°

Measure of angle F should be less than 180 = x/2°

By the triangle sum theorem, the Sum of measures of all interior angles of triangle = 180°

m(∠E) + m(∠F) + m(∠G) = 180°

55° + x/2° + x/2= 180°

x= 180° - 55°

x = 125

Measure of angle G = 125/2 = 62.5

Therefore, measure of angle G is 62.5°.

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The angle that the flagpole makes with the ground is 20°.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

Flagpole height = 16  feet

From figure  B,

The angle of elevation has increased this means,

The flagpole is leaning.

Now,

The angle that the flagpole makes with the ground.

Cos m = 15/16

Cos m = 0.9375

m = [tex]cos^{-1}[/tex] 0.9375

m = 20.36

m = 20°

Thus,

The angle that the flagpole makes with the ground is 20°.

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Answer:

b = -9

Step-by-step explanation:

-3 (3b + 6) = 36 - 3b

-9b - 18 = 36 - 3b

-6b - 18 = 36

-6b = 54

b = -9

Let's check

-3(3(-9) + 6) = 36 - 3(-9)

-3( -27 + 6) = 36 + 27

-3( -21) = 63

63 = 63

So, b = -9 is the correct answer.

Step-by-step explanation:

-3(3b+6)=36-3b

-9b-18=36-3b

-9b+3b=36+18

-6b=54

divide both sides by -6

b= -9

The properties are listed below.

Properties of addition and multiplication are defined for the various conditions and rules of addition and multiplication.  The properties are:

The product between any number and this one is zero. This comes from the existence of zero, which states that there must exist a value that represents nothingness, the zero.

This is the associative property of addition,

This is the reflexive property of equality, which says that every number is equal to itself.

This is the distributive property of addition which says ,

C*(A + B) = C*A + C*B

This is the inverse property of addition, this property says that for any real number x there exists a real number -x such that x+(-x)=0.

This is the symmetric property.

This is the transitive property, we can apply it in the next way

then x = z

This is the identity property of multiplication.

This is identity property of addition is that when a number n is added to zero, the result is the number itself i.e. n + 0 = n.

This is inverse property of multiplication. It states that if you multiply a number by its reciprocal, also called the multiplicative inverse, the product will be 1

Hence, the properties are identified.

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Answer:

64.34 feet.

Step-by-step explanation:

To solve this problem, we can use trigonometric ratios, specifically the tangent ratio.

Let's denote the height up the wall that the ladder reaches as "h". We can then set up the following equation:

tan(65°) = h/30

To solve for h, we can multiply both sides by 30:

30 tan(65°) = h

Using a calculator, we can find that tan(65°) is approximately 2.1445. Multiplying this by 30 gives us:

h ≈ 64.34 feet

Therefore, the ladder reaches approximately 64.34 feet up the wall. Rounded to the nearest hundredth of a foot, the answer is 64.34 feet.

A is the answer

tbtfhfhfshfgfsghgf

The area of a sector of a circle with radius 100 meters and central angle 1/8 radian is approximately 625 * π square meters.

The area of a sector of a circle with radius 100 meters and central angle 1/8 radian can be found using the formula:

A = [tex](\theta/2\pi )*\pi r^{2}[/tex]

where A is the area of the sector, Θ is the central angle in radians, π is Pi (approximately 3.14), and r is the radius of the circle.

Plugging in the given values, we have:

A = [tex](\frac{\frac{1}{8}}{{2\pi }} )*\pi *100^{2}[/tex]

A =[tex](1/16)*\pi *100^{2}[/tex]

A = [tex](\pi /16)*100^{2}[/tex]

A = (π/16) * 10000

A = 625 * π square meters

So, the area of the sector of the circle with radius 100 meters and central angle 1/8 radian is approximately 625 * π square meters.

The area of a sector of a circle is a portion of the circle's area enclosed by two radii and an arc. The central angle of the sector determines the fraction of the circle's circumference that the arc represents, and therefore the fraction of the circle's area that is enclosed by the sector.

To find the area of a sector, we first need to find the central angle in radians. The central angle is the angle formed by two radii at the center of the circle that intercept the circumference of the circle at the endpoints of the arc.

The formula for the area of a sector is given by:

A = [tex](\theta/2\pi )*\pi r^{2}[/tex]

where A is the area of the sector, Θ is the central angle in radians, π is Pi (approximately 3.14), and r is the radius of the circle.

In the given problem, the radius of the circle is 100 meters and the central angle is 1/8 radian. We plug these values into the formula and simplify to get the final answer.

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To determine how many cakes Lionel makes in one hour, we can use the following formula:

cakes per hour = total cakes / total hours worked

On Monday, Lionel made 7 cakes in some number of hours, so we don't know how many cakes he made per hour that day. However, on Tuesday, he made an additional 6 cakes (13 total cakes - 7 cakes made on Monday), and he worked for 2 hours longer than he did on Monday. Therefore:

cakes per hour on Tuesday = 6 cakes / 2 hours = 3 cakes per hour

So Lionel made 3 cakes per hour on Tuesday. We don't have enough information to determine how many cakes he made per hour on Monday.

Experimental Probability

Just because the odds are 50% for both genders doesn't mean there is any reason for it to be even. It's like flipping a coin six times. there's no reason for it to land on tails 3 times and heads 3 times. Its just more likely

it is not advisable to make only the minimum payment on a credit card if Jason wants to minimize the amount of interest he has to pay and pay off his debt faster.

A credit card is a payment card issued to users to enable the cardholder to pay a merchant for goods and services based on the cardholder's accrued debt.

Jason may not be doing the right thing by making only the minimum payment on his credit card, depending on the interest rate and penalty charges.

When a credit card holder makes only the minimum payment, the remaining balance accrues interest, which is added to the principal amount.

This means that the total amount owed on the credit card increases every month, even if no additional purchases are made.

The interest rate charged by the credit card company can significantly impact how much Jason ends up paying over time.

Hence, it is not advisable to make only the minimum payment on a credit card if Jason wants to minimize the amount of interest he has to pay and pay off his debt faster.

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The solution is, the required probability is p= 1/10.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

from the given information we get,

We have 5 possible parts colored red, green, blue, purple and yellow

The cube for this case have 6 possible numbers 1,2,3,4,5,6

We have the following even numbers: 2,4,6

Then the probability of obtain an even number is:

p1= 3/6= 1/2

Then the probability of obtain a blue color on the spinner is:

p2= 1/5

Then we want this probability:

Obtain an even number AND sppining a blue on the spinner

Then since the events are independent we can do this:

p = 1/2 * 1/5= 1/10

Hence, The solution is, the required probability is p= 1/10.

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Answer:28

Step-by-step explanation: because add z and x

The absolute value of the x-values of the coordinates of A and B = |2 - 5| = 3 units.

The absolute value of the y-values of the coordinates of B and C = |6 - 3| = 3 units.

If two points lie on a coordinate plane, the distance between them represents the length of the segment both points form, which is determined by finding the absolute difference between the values of their coordinates that lie on the same axis.

Given that a square has the points, A (2, 6), B (5, 6), C (5, 3), D (2, 3), its dimensions can be found as explained below:

Length of AB is found by calculating the absolute value of the x-values of the coordinates of A and B, while to find the length of BC, is the absolute value of the y-values of the coordinates of B and C.

Therefore:

AB = |2 - 5| = 3 units

BC = |6 - 3| = 3 units

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The interquartile range of the data is

The interquartile range (IQR) is a measure of variability in a dataset that is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).

The IQR is the range of the middle 50% of the data, and it provides a measure of the spread of the central part of the distribution.

From the given information, we have:

Minimum value = 4

Q1 = 11

Median = 14

Q3 = 16

Maximum value = 20

To find the IQR, we subtract Q1 from Q3:

IQR = Q3 - Q1 = 16 - 11 = 5

Therefore, the interquartile range of the data is 5.

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a. The probability that a person could give up her cell phone would be 0.69.

b. Probability that a person who could give up her cell phone could also give up television would be 0.45

c. The probability that a person who could not give up her ell phone could give up television would be 0.55.

d. Probability of giving up television is higher for people who could not give up their cell phone than for those who could give up their cell phone.

What is probability?

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

a. The probability that a person could give up their cell phone is the sum of the probabilities in the "Could Give Up" column: 0.31 + 0.38 = 0.69.

Therefore, The probability that a person could give up her cell phone would be 0.69.

b. The probability that a person who could give up their cell phone could also give up television is the conditional probability of "Could Give Up Television" given "Could Give Up Cellphone." This is calculated by dividing the joint probability of "Could Give Up Television" and "Could Give Up Cellphone" (0.31) by the probability of "Could Give Up Cellphone" (0.69): 0.31 / 0.69 = 0.4493 or approximately 0.45.

c. The probability that a person who could not give up their cell phone could give up television is the conditional probability of "Could Give Up Television" given "Could Not Give Up Cellphone." This is calculated by dividing the joint probability of "Could Give Up Television" and "Could Not Give Up Cellphone" (0.17) by the probability of "Could Not Give Up Cellphone" (0.31): 0.17 / 0.31 = 0.5484 or approximately 0.55.

d. To compare the probabilities of giving up television for people who could or could not give up their cell phone, we need to calculate the conditional probabilities of "Could Give Up Television" given "Could Give Up Cellphone" and "Could Give Up Television" given "Could Not Give Up Cellphone" respectively.

Probability of giving up television if one could give up a cell phone: 0.31 / 0.69 = 0.4493 or approximately 0.45.

Probability of giving up television if one could not give up a cell phone: 0.17 / 0.31 = 0.5484 or approximately 0.55.

The probability of giving up television is higher for people who could not give up their cell phone than for those who could give up their cell phone.

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The efficiency of the a and b from the uniform distribution on the interval a:X-1/2 and b:Xn-n/n+1 is x.

The probability distribution known as the uniform distribution comes in two varieties: the discrete case and the continuous case. Both types of uniform distributions, as their names imply, have constant or uniform probabilities for all possible values of the random variable.

The random sample X1,X2,....,Xn is taken from the uniform distribution on the interval (0,θ).

δlog(L(x,θ))/δθ = -n/θ + ∑(xt)/θ² = 0

n/θ = ∑(xt) /θ²

θ = x

Now derivate it again with respect to θ,

∂²log(L(x;θ)) / ∂θ²

=nθ²−2∑t(xt) / θ³<0

Since, the second derivative is less than 0, ^θ is maximum likelihood estimate of θ.

Therefore, the maximum likelihood estimate of θ is ¯x.

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Invested in each vehicle is $40,000 if the annual investment income is $944.25.

Let

CD's = x

Bonds = x + 60000

Stocks = y

x + x + 60000 + y = 140000 ----> 2x + y = 80000 .......(1)

Using I = Prt; t = 1; I = Pr

2x + 3.7(x + 60000) + 11.1y = 7800(100× )  × Since I used an exact proportion, the opposite side needs to be multiplied by 100.

5.7x + 11.1y = 558000 .......(2)

Either elimination or substitution;

x = 20000 y = 40000

So CD's = 20000, Bonds = 80000, Stocks = 40000

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The trigonometry ratio values are tan(50) = 1.19 and cos(70) = 0.34

This can be calculated using a calculator

So, we have

tan(50) = 1.19 and cos(70) = 0.34

This can be calculated using a calculator

So, we have

sin(84) = 0.9945 and tan(75) = 3.7321

Here, we make use of the laws of cosines and sines

So, we have

cos(X) = 15/17 = 0.8824

sin(C) = 36/45 = 0.8

Here, we make use of the laws of tangents and sines

So, we have

tan(?) = 6/13 = 0.4615

? = 24.77

sin(?) = 41/59 = 0.6949

? = 44.01

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The number of ordered triples (a, b, c) where a, b, and c are positive integers and a is a factor of b, a is a factor of c, and abc=N, is 64.

To find the ordered triplets, Firstly Factorize N into its prime factors.For each prime factor. we can choose its exponent as the value of a, b, and c. The total number of ordered triples (a, b, c) is (number of exponents + 1)^3.

let N = 24. The prime factorization of 24 is 2^3 * 3^1.

The number of possible values of a is 4 (from 0 to 3), so the number of possible values of b and c is also 4.

The number of ordered triples is 4^3 = 64.

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The scale factor that has been used is 1/2

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

Side length on red = 6 units

Corresponding side length on green = 3 units

Given that the red rectangle is the pre-image and the green rectangle is the image

We have

Scale factor = Green/Red

So, we have

Scale factor = 3/6

Evaluate

Scale factor = 1/2

Hence, the scale factor is 1/2

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Answer:

Solve for B:

[tex]B = -b+\frac{5A}{6h}[/tex]

Step-by-step explanation:

[tex]A=1.2h(b+B)[/tex]

Use the distributive property to multiply [tex]1.2h by b+B[/tex]

[tex]A=1.2hb+1.2hB[/tex]

Swap sides so that all variable terms are on the left hand side.

[tex]1.2hb+1.2hB=A[/tex]

Subtract [tex]1.2hb[/tex] from both sides.

[tex]1.2hB= A - 1.2hb[/tex]

The equation is in standard form.

[tex]\frac{6h}{5} B=-\frac{6bh}{5} +A[/tex]

Divide both sides by [tex]1.2h[/tex].

[tex]\frac{5*(\frac{6h}{5})B }{6h} =\frac{5(-\frac{6bh}{5}+A) }{6h}[/tex]

Dividing by [tex]1.2h[/tex] undoes the multiplication by [tex]1.2h[/tex].

[tex]B = \frac{5(-\frac{6bh}{5}+A) }{6h}[/tex]

Divide [tex]A - \frac{6hb}{5}[/tex] by [tex]1.2h[/tex].

[tex]B = -b+\frac{5A}{6h}[/tex]

Solve For B:

[tex]B = -b+\frac{5A}{6h}[/tex]

Answer:

Step-by-step explanation:

The equation that models the population of bats, y, after x years can be found using the formula:

y = P(1 + r)^x

where P is the initial population, r is the annual growth rate as a decimal, and x is the number of years.

In this case, the initial population P is 345,000, the annual growth rate r is 1.2% or 0.012 as a decimal, and x is the number of years. Substituting these values into the formula, we get:

y = 345,000(1 + 0.012)^x

Simplifying the expression in the parentheses, we get:

y = 345,000(1.012)^x

Therefore, the equation that models the population of bats, y, after x years is:

y = 345,000(1.012)^x

Step-by-step explanation:

the other answer is correct.

I just want to point out some mechanism used here :

the increase by 1.2%

an increase by x% means adding x% to the original 100%.

so, we end up with (100 + x)%.

"%" just stands for 1/100.

so, if y = 100%, an increase by x% is

y×(100 + x)/100 = y×(1 + x/100)

in our case here that is

345,000 × (1 + 0.012) = 345,000 × 1.012

and since the increase rate of 1.2% applies per year, we multiply the end population of every year by 1.012 for the following year.

so, each year a new factor of 1.012 is being integrated into the calculation.

it goes then

345,000×1.012×1.012×1.012×...×1.012 x times after x years.

and we get

y = 345,000 × (1.012)^x

Yes , the arithmetic sequence ( written as sequences of the form (a , a+k , a+2k , a+3k for some constants a and k ) is a subspace of V .

To determine whether subsets of V in the arithmetic sequences are subspaces of V, we check if they satisfy the three conditions for a subset to be a subspace:

(i) The subset must contain the zero vector.

(ii) The subset must be closed under vector addition.

(iii) The subset must be closed under scalar multiplication.

Let S be a subset of V consisting of arithmetic sequences.

Now we check the three conditions :

(i) We find an arithmetic sequence in S that has all its terms equal to zero. The only arithmetic sequence that satisfies this is the sequence (0, 0, 0, 0, ...), which is in S.

So , the subset "S" contains zero vector.

(ii) Next we need to show that if u and v are two arithmetic sequences in S, then their sum "u + v" is also an arithmetic sequence in S.

Let U = (a, a+k, a+2k, a+3k, ...) and V = (b, b+l, b+2l, b+3l, ...) be two arithmetic sequences in S.

Then, their sum is ⇒ u+v = (a+b, a+k+b+l, a+2k+b+2l, a+3k+b+3l, ...).

This is also an arithmetic sequence,

So , subset "S" is closed under vector addition.

(iii) Next , we show that if U is an arithmetic sequence in S and C is a scalar, then CU is also an arithmetic sequence in S.

Let U = (a, a+k, a+2k, a+3k, ...) be an arithmetic sequence in S, and let c be a scalar.

we get , CU = (ca, ca+ck, ca+2ck, ca+3ck, ...) is also an arithmetic sequence,

So , subset "S" is closed under scalar multiplication.

we see that , S satisfies all three conditions, it is a subspace of V.

Therefore, any subset of V consisting of arithmetic sequences is a subspace of V.

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The given question is incomplete , the complete question is

Let V be the space of all infinite sequences of real numbers , Which of the subsets of V in The arithmetic sequences [i.e. sequences of the form (a , a+k , a+2k , a+3k for some constants a and k] are subspaces of V ?

The shape of this histogram is skewed to the right since the highest frequency is found in the first class, and the frequencies decrease as the numbers increase.

The class width, also known as the class interval, is the difference between the upper and lower boundaries of a class. In this frequency distribution, the class width is 9 since the lower boundary of the first class is 54.5 and the upper boundary of the last class is 90.5. We can calculate the frequency of each class by counting how many numbers fall within the class boundaries. For example, the first class has 72 observations since there are 72 numbers that fall between 54.5 and 63.5. To calculate the relative frequency of each class, we divide the frequency of each class by the total frequency. For example, the relative frequency of the first class is 0.312 since 72/231 = 0.312. Once the frequencies and relative frequencies have been calculated, a histogram can be made to represent the data. The shape of this histogram is skewed to the right since the highest frequency is found in the first class, and the frequencies decrease as the numbers increase.

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