2020-2021 T-Math-Geo-T1-CBT: Section 2 - Calculator Section
Which of these correctly defines a ray?
a part of a line with exactly two end points
a straight path that extends endlessly in both directions
a circular path such that every point on the path is equidistant from its center
a part of a line that begins at a particular point and extends endlessly in one direction

Answer:

I think the answer is 4x^5z^8

Answer:

0.15

Step-by-step explanation:

3/20= 0.15

15/100= 0.15

Answer:

x = 4πn/3 x = 2π/3 4πn/3

Step-by-step explanation:

Answers in bold

\(\begin{array}{|c|c|} \cline{1-2}\text{number of rolls} & \text{number of people}\\\cline{1-2}1 & \boldsymbol{0.5}\\\cline{1-2}6 &3\\\cline{1-2}10 & \boldsymbol{5}\\\cline{1-2}16 & \boldsymbol{8}\\\cline{1-2}25 & \boldsymbol{12.5}\\\cline{1-2}n & \boldsymbol{0.5n}\\\cline{1-2}\end{array}\)

========================================================

Explanation:

The given table looks like this

\(\begin{array}{|c|c|} \cline{1-2}\text{number of rolls} & \text{number of people}\\\cline{1-2}1 & \\\cline{1-2}6 & 3\\\cline{1-2}10 & \\\cline{1-2}16 & \\\cline{1-2}25 & \\\cline{1-2}n & \\\cline{1-2}\end{array}\)

Focus on the row that has two values in it.

x = number of rolls = 6

y = number of people 3

k = constant of proportionality

y = kx

k = y/x = 3/6 = 0.5

The constant of proportionality is k = 0.5 which gives the direct variation equation of y = 0.5x

If x = 1, then y = 0.5*1 = 0.5 meaning that 1 roll feeds 0.5 people. This means we need 2 rolls to feed one person.

If x = 10, then y = 0.5x = 0.5*10 = 5 people can be fed with those 10 rolls. This process is continued until we finish filling out the table.

Answer:

  D.  m∠C = 34, b = 25, c = 16

Step-by-step explanation:

If all you want is an answer, your friendly triangle solver can provide it. (See below)

__

When you have two angles and a side length, the law of sines can be helpful.

  b/sin(B) = a/sin(A)

  b = sin(B)/sin(A)·a = sin(119°)/sin(27°)·13 ≈ 25.04 ≈ 25

Similarly, you have C = 180° -27° -119° = 34°, so ...

  c = sin(C)/sin(A)·a = sin(34°)/sin(27°)·13 ≈ 16.02 ≈ 16

These values match answer choice D.

  m∠C = 34, b = 25, c = 16

Answer:

1 makes 7 people full, 3 makes 5 people full

Step-by-step explanation:

1) A=b*h=33(22)=726 square inches. Would make 7 people full.

3)A=b*h=20(25)=500 square inches. Would make 5 people full

A bar chart is a graph that shows the differences in frequencies or percentages among categories of a nominal or an ordinal variable.

A bar chart is a commonly used graphical representation to display the distribution of data in different categories. It is particularly useful when working with nominal or ordinal variables, where the categories are distinct and unordered or have a specific order.

In a bar chart, each category is represented by a rectangular bar whose length corresponds to the frequency or percentage associated with that category. The height of the bar represents the magnitude or count of the variable in each category, allowing for easy visual comparison between the categories.

The bars in a bar chart can be arranged horizontally or vertically, depending on the preference or nature of the data. The chart may also include labels or annotations to indicate the category names or additional information.

By examining the lengths or heights of the bars in a bar chart, it becomes easy to identify the categories with the highest or lowest frequencies or percentages, as well as to compare the relative magnitudes among the different categories. This graphical representation aids in visualizing and interpreting the distribution of a nominal or an ordinal variable effectively.

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Answer: if its decimal and it wants you to round to next place to the tenths place

Step-by-step explanation: if it means to look at the hundredth's place to find your answer  if its bigger than five your second number will add up if its lower than five it stays the same

Answer:

g(x)     x^2 - 5

------ = ---------   where x ≠ - 1/4

f(x)         4x+1

Step-by-step explanation:

f(x) = 4x+1

g(x) = x^2 - 5

g(x)     x^2 - 5

------ = ---------  

f(x)         4x+1

The denominator cannot equal zero

4x+1 ≠ 0

4x≠-1

x≠-1/4

g(x)     x^2 - 5

------ = ---------   where x ≠ - 1/4

f(x)         4x+1

Answer:

I think it's D

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

we are trying to find miles so equation should start with m=

then if alberto is running 5 miles each week and then each week he increses it with 2 miles that can be written like this: 5w+2

so alll in all: C. m=5w+2

The rate of the reaction A+B⟶AB can be expressed as the rate constant, k, multiplied by the concentrations of reactants A and B. This is known as the rate equation, which is written as rate = k[A][B].

The rate equation for a reaction is used to determine the rate of reaction under specific conditions. The rate equation for the reaction A+B⟶AB is rate = k[A][B], where k is the rate constant and [A] and [B] are the concentrations of reactants A and B. The rate equation can be determined by performing experiments and analyzing the data. For example, in the table provided, three experiments were conducted to determine the rate of reaction. The concentrations of A and B were altered, and the time elapsed was measured. From this data, the rate of reaction could be determined by calculating the change in concentration of AB over the time elapsed. This rate could then be related to the concentrations of A and B, which results in the rate equation of rate = k[A][B].

[A] = 0.1M, [B] = 0.1M, and ΔtΔ[AB]​∣t=0​ = 2×10−4 mol L−1sec−1.

2×10−4 mol L−1sec−1/2×10−4 s = 1 mol L−1sec−1

rate = k[A][B].

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Answer:

6 nickels

Step-by-step explanation:

We'll let x=number of nickels in register

Then 5x=number of quarters

and (x-2)=number of dimes

and 30=number of pennies

Whatever monetary units we deal in (pennies, nickels, dollars, etc.), we have to be consistent. I choose to deal in pennies.

Now we know that the amt of money in nickels (x)(5)plus the amt of money in dimes(x-2)(10)plus the amt of money in quarters (5x)(25) plus the pennies (30) has to equal 850. (Remember, we are dealing in pennies). Thus, our equation to solve is:

5x+10(x-2)+5x(25)+30=850 Simplifying, we get:

5x+10x-20+125x+30=850 further simplifying, we get:

140x=840

x=6 nickels

5x=(5)(6)=30 quarters

and, of course, 30 cents

x-2=6-2=4 dimes

Hope this helps you! :)

Answer:

£14.29

Step-by-step explanation:

100-2= 98

98÷100=0.98

14÷0.98=14.2857142857

round it = £14.29

The fraction of the 30 cakes does Simon have left with os 7/10

A fraction is a part of a whole number, and a way to split up a number into equal parts.

Given that, Simon makes 30 cakes, he gives 1/5 of the cakes to Sali, he gives 10% of the 30 cakes to Jane,

We need to find, what fraction of the 30 cakes does Simon have left,

Number of cakes given to Sali = 1/5 of 30

= 30 / 5 = 6

That mean, Sali got 6 cakes out of 30.

Number of cakes given to Jane = 10% of 30

= 30 × 10/100

= 300 / 100

= 3

That mean, Jane got 3 cakes, out of 30.

The remaining number of cake = 30 - (6+3)

= 30 - 9

= 21

Therefore, the fraction of cakes left = 21 / 30

= 7/10

Hence, the fraction of the 30 cakes does Simon have left with os 7/10

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Answer:

$71.65

Step-by-step explanation:

3 rolls of flim cost $42.99 then for 1 roll of flim it will

cost ($42.99/3=$14.33)

therefore the cost of 5 rolls of flim will be (5×$14.33=$71.65)

Answ

Step-by-step explanation:

Two point slope =-(-6+6)/(6-2) =0

Equation is y+6 = 0(x-2)

y+6=0

y=-6

The point is -6 at y axis which is a horizontal line.

Answer:

plug in 1

answer is 6

Step-by-step explanation:

Answer:

f(1)=6

Step-by-step explanation:

(I'm not gonna simplify because this is just basic addition at this point)

The probability of getting 4 coins showing heads and 1 showing tails is approximately 15.625%.

When throwing the 5 identical coins, there are a total of 32 possible outcomes. This is because each coin has 2 possible outcomes (heads or tails), and since there are 5 coins, we multiply 2 by itself 5 times \((2^5 = 32).\)

To determine the probability of getting 4 coins showing heads and 1 showing tails, we need to calculate the number of favorable outcomes. In this case, we have 5 different ways to choose which coin shows tails (since there are 5 coins), and for each of those choices, there is only 1 possible outcome where that specific coin shows tails and the other 4 coins show heads.

So, the probability of getting 4 coins showing heads and 1 showing tails is 5/32.

To calculate the probability as a decimal or percentage, we simply divide 5 by 32:
5/32 ≈ 0.15625 ≈ 15.625%

Therefore, the probability of getting 4 coins showing heads and 1 showing tails is approximately 0.15625 or 15.625%.

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The coefficient of determination, denoted as R², is a statistic that measures the proportion of the variance in the dependent variable that is explained by the independent variables in a regression model.

The coefficient of determination, R², measures the goodness of fit of a regression model. It ranges from 0 to 1, with a higher value indicating a better fit. The calculation of R² involves comparing the variation in the dependent variable (represented by the total sum of squares, TSS) to the variation explained by the regression model (represented by the regression sum of squares, SSR). The formula for R² is SSR/TSS.

R² can be interpreted as the proportion of the total variation in the dependent variable that is accounted for by the independent variables included in the model. In other words, it tells us the percentage of the response variable's variability that can be explained by the regression model.

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This function can be represented as a the rational function y = 2 /x+2 that is option A.

In mathematics, a function is a relationship between two sets of elements, where each element of the first set (the domain) is associated with exactly one element of the second set (the range). In other words, a function is a rule that assigns to each input value from the domain a unique output value from the range.

Here,

To show that the given function can be represented as a rational function in the form y = A/(x+B), where A and B are constants, we need to perform partial fraction decomposition. Starting with the given function:

y = 2/(x+2)

We can write this as:

y = A/(x+2) + B

Where A and B are constants to be determined.

To solve for A and B, we can multiply both sides of the equation by the denominator of the first term, (x+2):

y(x+2) = A + B(x+2)

Now, we can substitute in values of x to solve for A and B.

Let x = -2:

y(-2+2) = A + B(-2+2)

y(0) = A

A = 2

Let x = 0:

y(0+2) = A + B(0+2)

y(2) = 2B + A

Substitute A = 2:

y(2) = 2B + 2

Solve for B:

y(2) - 2 = 2B

y(2) - 2 = 2/(2+2)

y(2) - 2 = 1/2

2B = (1/2) - 2

B = -3/4

Therefore, we have found that:

y = 2/(x+2) - 3/4

which can be written as:

y = (8-3x)/(4(x+2))

So the answer is (a) x+2.

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Answer:

The unit rate for miles per gallon is 30 3/5

miles per gallon

Step-by-step explanation:

To get the unit rate for miles per gallon, we simply divide the number of moles by the amount of gallons

Number of miles is 38 1/2 which is 77/2 miles

Number of gallons = 1 1/4 = 5/4

So unit rate will be;

77/2 divided by 5/4

= 77/2 * 4/5 = 154/5 = 30 3/5 miles per gallon

Answer:

x < 15

Step-by-step explanation:

we want to isolate x, so we get rid of the 3, that is being divided by 2x, we take it to the other side to multiply.

2x < 10 x 3

2x < 30

we move the 2 that is multiplying x to the other side, since it was multiplying, we make inverse operations and now the 2 will divide 30

x < 30 ÷ 2

x < 15

Answer:

x=15 or false

Step-by-step explanation:

In order to find x you have to get the x by itself. To do this you multiply 3 on both sides this gives you 2x<30. Then you divide by 2, this gives you x=15. Then in order to find whether or not the inequality is true you have to plug x back in. 2(15)/3<10 is equal to 30/3=10 which leads to 10<10, which is false.

The second number used by Ameekah to represent the consecutive integers is (x + 1).

Let 'x' be the first number written by Ameekah.

Then, the second number will be obtained by adding one to first number.

= x + 1

Thus, the second number used by Ameekah to represent the consecutive integers is (x + 1).

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Answer:

"B" is correct, "x + 1"

Step-by-step explanation:

Have a Jocular Day

Answer:

Each side is 15 ft

Step-by-step explanation:

The area of a square is given by

A = s^2 where s is the side length

225 ft^2 = s^2

Take the square root of each side

sqrt ( 225 ft^2) = sqrt ( s^2)

15 ft = s

Each side is 15 ft

Answer:

c  (2,0)

Step-by-step explanation:

One way to solve this system of inequalities is to graph the inequalities and see which ordered pair lies in the shaded region that is common to both inequalities

See the graph and each of the ordered pairs. Only (2, 0) lies entirely within the shaded region

(-1, 0) lies on the intersection of the two lines so it will satisfy the >= inequality but not the < inequality

Answer (2, 0)

However if you cannot use graphing then a brute force method must be used to see which ordered pair satisfies both inequalities

a. (-1, 0)
Check y < 2x + 2 ?
=>  0 < 2(-1) + 2 ?
=> 0 < -2 + 2
0 < 0 ? False
Eliminate option a

b. (0, 3)
y < 2x + 2?
=> 3 < 2(0) + 2?
3 < 2? False
Eliminate option b

c. (2, 0)
y < 2x + 2?
=> 0 < 2(2) + 2 ?
=>  0 < 4 + 2
=> 0 < 6 True

Move to the second inequality
y ≥ -x - 1?
0 ≥ -2 - 1
0 ≥ -3 True

So option c is the correct choice

While it is not necessary to check option d, let's do it anyway
d. (-1, -4)
y < 2x + 2 ?
-4 < 2(-1) + 2 ?
-4 < -2 + 2 ?
-4 < 0 ? True

Move to the second inequality
y > -x - 1 ?
-4 > -(-1) - 1
-4 > -2? False
Option d is eliminated

Correct answer: (2, 0) which is option c

Answer:

The vertex is at (2, 8) and the axis of symmetry is x = 2

Step-by-step explanation:

First, let's find the zeros of the equation

Factor the equation

-2x² + 8x = -2x(x - 4) = 0

-2x = 0

x - 4 = 0

h(x) is 0 when x = 0 or 4

Now we add those zero's together and divide by 2 to find the middle (the axis of symmetry)

4 + 0 = 4

4 ÷ 2 = 2

Now plug 2 into the original equation to find the vertex

h(x) = -2(2)² + 8(2) = 8

Since h(x) equals 8 at the axis of symmetry, which is 2, our vertex is (2,8)

The correct statement concerning the vertex and axis of symmetry of

h(x) = −2x^2 + 8x is:

The vertex is at (2, 8) and the axis of symmetry is x = 2.

Option C is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The correct statement concerning the vertex and axis of symmetry of

h(x) = −2x^2 + 8x is:

To find the vertex and axis of symmetry of a quadratic function in standard form (y = ax² + bx + c), we can use the formulas:

x = -b / 2a (for the x-coordinate of the vertex)

y = (c - b²) / 4a (for the y-coordinate of the vertex)

and

x = -b / 2a (for the equation of the axis of symmetry)

In this case,

a = -2, b = 8, and c = 0.

Substituting these values into the formulas above, we get:

x = -8 / 2(-2) = 2 (x-coordinate of vertex)

y = 0 - 8² / 4(-2) = 8 (y-coordinate of vertex)

x = 2 (equation of the axis of symmetry)

Therefore,

The vertex is at (2, 8) and the axis of symmetry is x = 2.

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The answer to the best point estimate for the population's variance when the sample variance is 38.4 is 38.4.

Point estimate: The estimated value of a population parameter is a point estimate.

Sample variance: Sample variance is an estimate of the population variance that is obtained by measuring the squared deviations of the sample values around the sample mean.

Variance: The variance is a measurement of the variability of the data, which is calculated as the mean of the squares of the deviations of each data point from the mean of the data. 

Steps to determine the point estimate for the population's variance: The best point estimate for the population's variance is the sample variance.

Given, Sample variance = 38.4.

Hence, the best point estimate for the population's variance is 38.4.

Therefore, the answer is 38.4.

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