The length of a circle's radius where the diameter's endpoints are at (2,4) and (-3,-1) is 5/2.
What is meant by radius?The radius of a circle is the separation between any two points on its circumference. R or r is typically used to indicate it. This amount is significant in practically all formulas involving circles. A circle's radius can also be used to calculate its surface area and circumference. Circle circumference equals 2π (Radius). A radius is a segment of a line having one terminus in the centre and the other on the circle. Radius = Circular Diameter: The diameter of a circle is defined as the length of a line segment with its endpoints on the circle and passing through its centre. Radius 2 = diameter.Then,
[tex]$D=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
As a result, the diameter's end points are (2,4) and (-3,-1)
[tex]d=\sqrt{(-3-2)^2+(-1-4)^2}[/tex]
[tex]d=\sqrt{(-5)^2+(-5)^2}[/tex]
[tex]\mathrm{d}=\sqrt{25+25}=\sqrt{50}=5 \sqrt{2}[/tex]
[tex]$\text { We know Radius } & =\frac{\text { Diameter }}{2} \\[/tex]
[tex]$& =\frac{5 \sqrt{2}}{2}=\frac{5}{\sqrt{2}}[/tex]
Hence, the radius of given circle is [tex]$} \Rightarrow \frac{5}{\sqrt{2}}[/tex]
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please explain what comparison you can state about the two angles and explain how you can draw that conclusion
The conclusion about angles B and C is that the angles are equal angles
How to determine the true statement?
The given parameters are:
Angle A and Angle B are supplements
Angle A and Angle C are supplements
Supplementary angles add up to 180 degrees.
This means that
A + B = 180
A + C = 180
Subtract the two equations
So, we have
A - A + B - C = 180- 180
Evaluate the like terms
So, we have
B - C = 0
Add C to both sides
B = C
Hence, both angles are congruent angles
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Ready
How do you find the distance between
the points shown?
Add the distance between
each point and the y-axis.
What is the distance between
point A and point B?
units
A(-8,-4)
B (2,-4)
Answer:
10 units
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
To find the distance between two points, substitute the given points into the distance formula and solve for d.
Given points:
A (-8, -4)B (2, -4)[tex]\begin{aligned}\implies d&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(2-(-8))^2+(-4-(-4))^2}\\&=\sqrt{(10)^2+(0)^2}\\&=\sqrt{100}\\&=10\end{aligned}[/tex]
However, as the y-values of the two given points are the same, we can simply find the difference between the x-values of the two points to find the distance between point A and B:
[tex]\begin{aligned}\implies \textsf{Distance}&=x_B-x_A\\&=2-(-8)\\&=2+8\\&=10\end{aligned}[/tex]
Therefore, the distance between point A and point B is:
10 unitsThe x and y -intercepts of a line are -5/3 and 3/5 respectively. What is its equation?
The equation of the line whose x and y -intercepts are -5/3 and 3/5 respectively is [tex]9x - 25y + 15 = 0\\[/tex] .
Given,
The x-intercept of a line = -5/3
The y-intercept of a line = 3/5
by substituting values in the intercept form of a line:
[tex]-\frac{3x}{5} + \frac{5y}{3} = 1\\[/tex]
On multiplying the equation by 15 both L.H.S. & R.H.S.
[tex]-9x + 25y = 15[/tex]
⇒ [tex]9x - 25y + 15 = 0\\[/tex]
Therefore, the Equation of line is [tex]9x - 25y + 15 = 0\\[/tex] .
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1
Which of the following lists the terms in
x^2-7x + 11?
A. x, 7, 11
B. x², -7x, 11
C. x, -7x, 7, 11
D. x, x², 7, -7x, 11
The equation is x² - 7x+11 is in form of quadratic equation ax²+bx+c where a = x² , b = -7 and c = 11 .
Option B is correct.
How do quadratic equations work?Quadratic equations are second-degree algebraic expressions with the form ax² + bx + c = 0. The word "quadratic" comes from the word "quad," which means square. To put it another way, an "equation of degree 2" is a quadratic equation. Numerous situations call for the use of a quadratic equation.
Evaluating :Factoring x²-7x+11
The first term is, x² its coefficient is 1 .
The middle term is, -7x its coefficient is -7 .
The last term, "the constant", is 11
x² - 7x + 11 = 0
Why do we use quadratic equations?When two things are multiplied together and both depend on the same variable, quadratic equations are frequently used. A quadratic equation is used, for instance, when working with area when both dimensions are written in terms of the same variable.
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The impedance Z, in ohms, of a circuit element is defined as the ratio of the phasor voltage V, in volts, across the element to the phasor current I, in amperes, through the elements. That is, z= v/i. If the voltage across a circuit element is 12+5i volts and the current through the element is 3-2i amperes, determine the impedance.
The impedance of the circuit in this problem is given as follows:
Z = (26 + 39i)/11.
How to obtain the impedance of a circuit?The impedance of a circuit of Voltage V and Current I is given by the equation presented as follows:
Z = V/I.
The parameters for this problem are given as follows:
V = 12 + 5i.I = 3 - 2i.Hence the impedance is given as follows:
Z = (12 + 5i)/(3 - 2i).
Removing the complex number from the denominator, we have that:
Z = (12 + 5i)/(3 - 2i) x (3 + 2i)/(3 + 2i)
Z = [(12 + 5i)(3 + 2i)]/11
11 because (3 - 2i)(3 + 2i) = 9 - 2i² = 9 + 2 = 11, as i² = -1.
Hence:
Z = (36 + 39i - 10)/11
Z = (26 + 39i)/11.
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rewrite 9x2 + 3xy + 15x + 5y in factored form. (3x + 3)(5x + y) (3x + 5)(3x + y) (3x + 5y)(3x + 1) (3x + y)(5x + 3)
The given equation 9x2 + 3xy + 15x + 5y in factored form is[tex](3 x+y)(3 x+5)$$[/tex]
What is factored form?The factored form of a quadratic expression is one in which the quadratic expression is the product of two factors, each of which is a linear expression. By extending it, which entails multiplying out the factors, a factored expression can be restated in standard form. Y=12(x-6)(x+2) is an illustration of a factored quadratic function. The graph's x-intercepts and vertex can both be determined by analyzing this form. The four primary methods of factoring are the Grouping method, the Difference in Two Squares, the Sum or Difference in Cubes, and the Greatest Common Factor (GCF).
Factor [tex]$9 x^2+3 x y+15 x+5 y:[/tex]
Steps
[tex]& 9 x^2+3 x y+15 x+5 y \\[/tex]
[tex]& =\left(9 x^2+3 x y\right)+(15 x+5 y)[/tex]
Factor out 3 x from [tex]$9 x^2+3 x y: \quad 3 x(3 x+y)$[/tex]
Factor out 5 from[tex]$15 x+5 y: \quad 5(3 x+y)$[/tex]
[tex]$$=3 x(3 x+y)+5(3 x+y)$$[/tex]
Factor out common term[tex]$3 x+y$[/tex]
[tex]$$=(3 x+y)(3 x+5)$$[/tex]
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Ms. Morales bought the kiddie pool shown below for her children. pleas help thank you
A diagram of a kiddie pool is shown. The height of the pool is labeled twelve inches. A line drawn under the pool from one side of the pool to the other is labeled fifty-four inches.
If she filled the pool 3/4 of the way with water, how much water did Ms. Morales put in the pool in terms of π?
Responses
A)5,832π in.3
B) 6,561π in.3
C) 7,776π in.3
D) 8,748π in.3
The water Ms. Morales put in the pool in terms of π is [tex]\pi[/tex]6561inch^3
What is the volume of a right circular cylinder?Suppose that the radius of considered right circular cylinder be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.
Given;
Diameter= 54 in.
Height of pool= 12ft
Now,
3/4 th height of pool;
3/4 x 12= 9inch
Volume= [tex]\pi r^{2}h[/tex]
=[tex]\pi[/tex]27x27x9
=[tex]\pi[/tex]6561inch^3
Therefore, the volume of pool will be [tex]\pi[/tex]6561inch^3
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a cube has edge length 2. suppose that we glue a cube of edge length 1 on top of the big cube so that one of its faces rests entirely on the top face of the larger cube. then find the percent increase in the surface area (sides, top, and bottom) from the original cube to the new solid formed.
The total surface area is 28 square units.
Each of the 6 faces in the original cube has an area of 2* 2 = 4 square units. Thus, the original figure's surface area as a whole was 24 square units.
The new figure has the same surface area as the old one, plus six new faces that each have an area of one dollar per square unit, for a total surface area increase of six dollars. However, the 1 square unit of the bigger cube's top and the 1 square unit of the smaller cube's bottom are not surfaces and do not contribute to the surface area.
This results in a total surface area of 24 + 6 - 1 - 1 = 28 square units.
Therefore, The total surface area is 28 square units.
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Lines L and M are perpendicular to each other. Line L has an undefined slope. Find the possible equation of line M.
y=7 is One of line M's potential equations.
Let L and M be two lines that are perpendicular to each other. Slope of line is given by m=x 2 −x 1/ y 2 −y 1
If the denominator is zero, or if the value of the x-coordinate is the same at all points, the value of m is undefined. Every point lying on L has the same value of the x-coordinate because L has an undefined slope.
L is a vertical line because it is parallel to the Y-axis.
Lines that are vertical and horizontal are perpendicular to one another.
∴ Line M will be parallel to the X-axis since it is perpendicular to line L.
Every point located on M will have a constant y-coordinate.
∴ m=0 for M.
Thus, y=7 is one of line M's potential equations.
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harold tosses a nickel four times. then find the probability that he gets at least as many heads as tails.
As a result, there is an 11/16 chance that there will be at least as many heads as tails.
What is probability?The branch of mathematics concerned with probability is known as probability theory. Although there are several different interpretations of probability, probability theory treats the concept rigorously mathematically by expressing it through a set of axioms. The probability is a measure of the likelihood that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula. A probability is a number that represents the likelihood or chance that a specific event will occur. Probabilities can be expressed as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Here,
The likelihood that there will be more tails, more heads, or equal numbers of each is 5/16, 5/16, and 6/16, respectively. Therefore, the probability that there will be at least as many heads as tails is 11/16.
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Complete Question:
Harold tosses a nickel four times. The probability that he gets at least as many heads as tails is:
For the reaction A + B -> C, explain at least two ways in which the rate law could be zero order in chemical A.
Chemical A's rate law may be zero order and is unaffected by the ratio of reactant to product concentrations.
What is meant by ratio?When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls). This suggests that there are more individuals who disapprove of your opinion than who approve of it.The mathematical formula for the ratio is commenting/(reposts + likes), where the ratio is the number of comments a post receives in comparison to likes and reposts.For the zero order reaction, [tex]$\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}$[/tex]
Rate equation is : Rate [tex]$=\mathrm{k}[\mathrm{A}]^0[\mathrm{~B}]^0$[/tex]
As a result, the pace of the reaction is unaffected by the amounts of reactant and product present.
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1850-120w=b (the answer of part A)
How would you interpret the statement that b(14)=170?
The statement b(14) = 170 is interpreted using the function 1850 - 120w = b to be:
When w is 14 b is equal to 170
How to interpret a functionThe function 1850 - 120w = b as in the problem is a linear function.
A linear function is one which all the parameters has exponents of one. In the linear function parameters are defined below
b = the output value
w = the input value
120 = slope
1850 = the y intercept
The statement b(14) = 170 means that at input of 14 the out put is 170. this is shown mathematically
1850 - 120w = b
1850 - 120 * 14 = b
1850 - 120w = 170 = b
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An individual was making blankets for a few friends. The individual used 6.25 feet of fabric for one blanket. If the individual makes 7 blankets, how many feet of fabric will the individual have used to make 7 blankets (round to the nearest whole number)?
|x+3|=7
solve
pls show work
Answer: x=4
Step-by-step explanation:
Firstly, x+3 is in absolute value and absolute value basically turns that into positive, which brings us to x+3=7. Now, use your basic algebra skills to subtract 3 form both sides and get x=4. Hope this helps!
Answer:
Two roots: -10 and 4
Step-by-step explanation:
Since the expression inside the modular brackets can be positive or negative, the equation can have two different roots. And it is solved for the positive and negative options.
Positive option:
x+3=7
x=7-3
x=4
Negative option:
x+3=-7
x=-7-3
x=-10
(a) If you invest Po dollars at 7% annual interest and the future value is computed by continuous com- pounding, how long will it take for your money to double?
(b) Suppose you invest Po dollars at r% annual interest and the future value is computed by continuous compounding. If you want the value of the account to double in 2 years, what is the required interest rate?
(c)A rule of thumb used by many people to determine the length of time to double an investment is the rule of 70. The rule says it takes about t = 70/r years to double the investment. Graphically compare this rule to the one isolated in part b. of this problem.
(a) It will take approx 10.2 years to double your principal at 7% interest.
(b) The required rate of interest to double our income in 2 years is approx 44%
(a) Given,
Annual rate of interest = 7%
Let the principal be [tex]x[/tex].
Formulae for compound interest :
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Substituting the value of [tex]P , r , n[/tex] in above formulae.
[tex]2P = P(1 + \frac{r}{n})^{nt}\\\\2x = x(1 + \frac{0.07}{1})^{1t}\\\\2 = 1.07^{t} \\\\t=\frac{ln(2)}{ln(1.07)\\}\\\\t = 10.244768[/tex]
Therefore, it took approx. 10.2 years to double your principal at 7% interest.
(b) Given,
The annual rate of interest = [tex]r[/tex]%
Let the principal be [tex]x[/tex].
Formulae for compound interest :
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
we want our money to double in 2 years
[tex]2P = P(1 + \frac{r}{n})^{nt}\\\\2x = x(1 + \frac{r}{1})^{2}\\\\2 = (1+r)^{2} \\\\\sqrt{2} = 1 + r\\\\r=0.44[/tex]
Therefore, the required Rate of interest is approx 44%.
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Which of these strategies would eliminate a variable in the system of equations?
{
6
�
+
5
�
=
1
6
�
−
5
�
=
7
⎩
⎪
⎪
⎨
⎪
⎪
⎧
6x+5y=1
6x−5y=7
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
Subtract the bottom equation from the top equation.
(Choice B)
B
Add the equations.
(Choice C)
C
Multiply the top equation by
7
77, then subtract the bottom equation from the top equation.
Answer:
B
Step-by-step explanation:
If both signs are the same (++,--), then you subtract.
If the two signs are different(+-,-+), then you add.
Which expression shows the first step in evaluating
2+7.12-3²?
6
A 2+84-3²
6
B 9.12-3²
C 2+7.122
1.12-9
6
D 2+7.2-3²
The first step in evaluating 2+7. 12/6-3² is to substitute the values for the numbers and calculate the sum of 2+7, which is 9.
What is evaluating?Evaluating is the process of making judgments about something based on a set of criteria. It involves analyzing and assessing a subject and making a determination of its value or worth. This can be done for a variety of things, such as an essay, a project, an individual or group, or a product. Evaluation is a crucial part of the decision-making process and involves a careful consideration of all relevant information and factors. It helps to identify strengths and weaknesses, and determine the effectiveness of something. Evaluating is also used to measure performance, identify areas for improvement, and make comparisons.
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What is the end behavior of the graph?
The end behaviour of the graph shows that the range of the graph ranges from 0 to ∞.
What are domain and range?The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f. (x). A function's range is the set of values that the function can take. This is the set of values that the function returns after we enter an x value.
In the given image the graph is showing a parabola symmetric about the y-axis. The range of the graph is varying from 0 to ∞. The graph's end behaviour indicates that the graph's range is from 0 to.
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In a certain school district, it was observed that 33% of the students in the element schools were classified as only children (no siblings). However, in the special program for talented and gifted children, 130 out of 345 students are only children. The school district administrators want to know if the proportion of only children in the special program is significantly different from the proportion for the school district. Test at the α=0.05α=0.05 level of significance. What is the hypothesized population proportion for this test?
The null hypothesis population proportion for this test is 33%. The test is used to determine if the proportion of only children in the special program is significantly different from the proportion for the school district, at an alpha level of 0.05.
Step 1: Define the parameters:
Population proportion (p): 33%
Significance level (α): 0.05
Step 2: Calculate the test statistic:
Sample proportion (p-hat): 130/345 = 0.37
Step 3: Calculate the critical value:
Critical value (α): 0.05
Step 4: Compare the test statistic to the critical value:
Test statistic (p-hat) > Critical value (α): 0.37 > 0.05
The test statistic is greater than the critical value, so the null hypothesis is rejected. Therefore, the proportion of only children in the special program is significantly different from the proportion for the school district.
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Classify each histogram using the appropriate descriptions. Identify all of the descriptions that apply for each histogram.
The categories include,
8th grade: left-skewed unimodal
Unimodal and symmetric birth weight
Computer count is unimodal and skewed to the right.
Bimodal adult weight distribution
Describe the histogram?A graph called a histogram shows the frequency distribution of a few data points for a single variable. Data is frequently divided into a number of "bins" or "range groups" by histograms, which count the number of data points in each bin.
While bar charts show categorical factors, histograms display numerical or quantitative data. In most situations, a histogram's numerical data will be continuous (having infinite values). To attempt to plot a continuous variable's possible values on an axis would be absurd.
Based on the frequency distribution, there are four different types of histograms.
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The complete question is: Classify each histogram using the appropriate descriptions. Identify all of the descriptions that apply for each histogram.
30 divided by 0.25?????????????????? I need step by step explanation!!!!
Answer:
120
Step-by-step explanation:
This is simply because 0.25 is 1/4 and 30 ÷ 1/4 is the same as 30 × 4/1 which equals to 120
Answer:
120
Step-by-step explanation:
multiply 100 in the numerator and denominator to remove the decimal point.2
30×100/0.25×100
=3000/25
=120
Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.
y = sin(x), y = 0, 0 ≤ x ≤ ????; about y = −5
The upper limit of y is not given, the integral cannot be evaluated at this point.
The volume of the solid obtained by rotating the region bounded by the given curves about the specified line can be determined by the following integral:
V = ∫-5^y [π(y-sin(x))^2]dx
The integral is set up by breaking the region up into slices that are perpendicular to the y-axis. The width of each slice is equal to dy and the height of each slice is equal to the area of the cross-section of the solid, namely π(y-sin(x))^2. The integral is then evaluated from the lower limit of y=-5 to the upper limit of y, which is determined by the equation of the given curve, y=sin(x). As the upper limit of y is not given, the integral cannot be evaluated at this point.
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A kite has angle measures of 7x°, 65°, 85°, and 105°. Find the value of x.
Which of the angles are opposite angles? Explain your reasoning.
Part 1
Angles of a quadrilateral add to 360 degrees.
[tex]7x+65+85+105=360\\\\7x+255=360\\\\7x=105\\\\x=15[/tex]
Part 2
If [tex]x=15[/tex], then [tex]7x=105^{\circ}[/tex]. Thus, the angles measuring [tex]7x[/tex] and [tex]105^{\circ}[/tex] are opposite angles since opposite angles of a kite are congruent.
This means the remaining angles, which are the angles measuring [tex]65^{\circ}[/tex] and [tex]85^{\circ}[/tex], are also opposite using the process of elimination.
Use the figure showing two parallel lines cut by a transversal. Find the measure of angle 2 if the measure of angleUse the figure showing two parallel lines cut by a transversal. Find the measure of angle 2 if the measure of angle 1 is 65 degrees.
1 is 65 degrees.
The measure of angle 2 is given as follows:
115º.
What are linear pairs?When two parallel lines are cut by a transversal, the consecutive angles relative to the same vertex are linear pairs, which are supplementary angles.
When two angles are supplementary, the sum of their measures is of 180º, meaning that the equation for this problem is given as follows:
m < 1 + m < 2 = 180º.
Since m < 1 = 65º, the measure of angle 2 is obtained as follows:
m < 2 = 180 - 65
m < 2 = 115º.
Missing InformationThe figure giving context to the problem, without scaling, is given at the end of the answer.
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assume a member is selected at random from the population represented by the graph. find the probability that the member selected at random is from the shaded region of the graph. assume the variable x is normally distributed.
0.30 is the probability that the member selected at random is from the shaded region of the graph. assume the variable x is normally distributed.
What is probability and example?
Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .
Remember that
z =(x - μ)/σ
where
μ=509
σ=121
so
Find out the value of Z for x=200
Z =(200 - 509)/121
Z=-2.5537
Find out the value of Z for x=450
Z=(450-509)/121
Z=-0.4876
Hence, 0.30 is the probability that the member selected at random is from the shaded region of the graph. assume the variable x is normally distributed.
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A person cycles from their home to a library which is 8 kilometers away. It takes them 20 minutes to reach the library. They stay there for 30 minutes to read, and then walk to their friend's home which is 4 kilometers from the library and reach there in 20 minutes. Which graph best represents this situation?
It’s cAnswer:
Step-by-step explanation:
it’s right
The graph that represents the situation is added as an attachment
How to determine the graph of the situationFrom the question, we have the following parameters that can be used in our computation:
Library = 8 kilometers for 20 minutesTime at rest = 30 minutesFriend = 4 kilometers for 20 minutesThis means that the graph would be represented using a distance/time graph
Such that the distance would be on the y-axis and the time would be on the x-axis
See attachment for the graph
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There are 4 apples, 3 peaches and 2 plums in a grocery bag. If the the checkout person picks 2 plumbs and 1 peach out of the bag, what is the probability that the next piece of fruit out of the bag will be an apple? (Give your answer as a fraction in simplest form.)
The probability that the next piece of fruit out of the bag will be an apple is ²/₃.
What is the probability?The probability is the chance that an expected outcome occurs out of many possible outcomes.
Probability is a fractional value that is obtained as the quotient of the expected outcome over the total events.
The number of apples = 4
The number of peaches = 3
The number of plums = 2
Total number = 9
The number of fruits taken out = 3 (2 plumbs and 1 peach)
The remaining fruits in the grocery bag:
The number of apples = 4
The number of peaches = 2 (3 - 1)
The number of plums = 0 (2 - 2)
Total number = 6
The probability of picking an apple out of the remaining fruits = 4/6 = 2/3
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Landon had one string that was 10 meters long. He used 6.275 meters of this string for a project.
What was the length of string in meters that Landon had left?
16.275 m
4.275 m
3.725 m
6.265 m
Answer:
3.725
Step-by-step explanation:
10-6.275
4-0.275
3.725
the three interior angles of a triangle measure x°, (x+5)°, and (x+25)°, which is the measure of the three angles
* 45°
* 65°
* 70°
* 50°
Answer:
*50
Step-by-step explanation:
Sum of the interior angle
(n - 2) 180
From the question n is 3.
=(3 - 2) 180
=(1) 180
=180
The value of x
x + (x + 5) + (x + 25) 180
=x + x + x + 5 + 25 = 180
=3x + 30 = 180
=3x = 180 - 30
=3x = 150
=3x/3 = 150/3
x = 50
Therefore the value of x is 50.
let $x$ be a real number selected uniformly at random between 100 and 200. if $\lfloor \sqrt{x} \rfloor
The value of [tex]$\lfloor \sqrt{X} \rfloor$[/tex] can be any number between 10 and 13, since 14 is not an integer.
Let x be the random variable denoting the real number selected uniformly at random between 100 and 200.
The square root of [tex]$X$, $\sqrt{X}$,[/tex] will be a real number between 10 and 14. The floor function, [tex]$\lfloor \sqrt{X} \rfloor$[/tex] will take the integer less than or equal to[tex]$\sqrt{X}$.[/tex]This means that the value of [tex]$\lfloor \sqrt{X} \rfloor$[/tex] can be any number between 10 and 13, since 14 is not an integer.
For example, if [tex]$X = 150$[/tex], then [tex]$\sqrt{X} = 12.25$[/tex], so [tex]$\lfloor \sqrt{X} \rfloor = 12$[/tex]
In summary, for any real number selected uniformly at random between 100 and 200, the value of[tex]$\lfloor \sqrt{X} \rfloor$[/tex] is any number between 10 and 13.
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