Answer:
age of father is 40 and son is 10
Step-by-step explanation:
let age of father be x
and age of son is y
At present,
x+y=50 eq 1
After 5 years,
Ages are,
Father = x+5
Son = y+5
As age of father is thrice so,
x+5 = 3(y+5)
x+5 = 3y+15
x-3y= 10 eq 2
Multiply eq 1 by 3
3x + 3y = 150 eq 3
Now, Add eq 2 and 3
4x = 160
x = 40 .................... ....... Age of father
Put x in eq 1
40 + y = 50
y = 10 ......................... Age of Son
witney peter, a professional dart player has a seventy percent chance of hitting the bull's eye on a dartboard with and throw. assume that that the throw of a dart is independent. what is the probability that pete hits five or fewer of his next ten shots?
Without spectacles, Witney Pete has a 5/10 chance of hitting the bullseye. Witney Pete could strike the bullseye with his spectacles 0.7 of the time. This likelihood is far higher than hitting the bullseye without glasses. the probability that Pete hits five or fewer of his next ten shots is approximately 2.487.
What is the probability that Pete hits five or fewer of his next ten shots?Generally, To find the probability that Pete hits five or fewer of his next ten shots, we need to find the probability that he hits exactly 0, 1, 2, 3, 4, or 5 bull's eyes.
The probability that Pete hits exactly k bull's eyes in n throws is given by the binomial distribution:
P(k bull's eyes in n throws) = (n choose k) * p^k * (1-p)^(n-k)
where p is the probability of hitting a bull's eye on a single throw and n choose k is the binomial coefficient, which is equal to n!/(k!(n-k)!).
Substituting the given values, we get:
P(0 bull's eyes in 10 throws) = (10 choose 0) * (0.7)^0 * (0.3)^10 = 0.028 P(1 bull's eyes in 10 throws) = (10 choose 1) * (0.7)^1 * (0.3)^9 = 0.189 P(2 bull's eyes in 10 throws) = (10 choose 2) * (0.7)^2 * (0.3)^8 = 0.462 P(3 bull's eyes in 10 throws) = (10 choose 3) * (0.7)^3 * (0.3)^7 = 0.605 P(4 bull's eyes in 10 throws) = (10 choose 4) * (0.7)^4 * (0.3)^6 = 0.501 P(5 bull's eyes in 10 throws) = (10 choose 5) * (0.7)^5 * (0.3)^5 = 0.302
The probability that Pete hits five or fewer bull's eyes in his next ten shots is the sum of the probabilities of hitting exactly 0, 1, 2, 3, 4, or 5 bull's eyes:
P(hitting 5 or fewer bull's eyes in 10 shots) = 0.028 + 0.189 + 0.462 + 0.605 + 0.501 + 0.302 = 2.487
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The weight of 2apple i 400 gram. I ate one apple of 150 gram. Find the weight of the other apple
The weight of the other apple is 250 grams.
As per the given data:
The weight of 2 apples is 400 gram.
The weight of 1 apple is 150 grams which I ate.
We have to determine the weight of the other apple.
Subtract the weight of 1 apple from weight of 2 apples
Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers
One value is 400 and the other value is 150.
Means subtract 150 from 400.
The weight of the other apple = Weight of 2 apples - The weight of 1 apple
= 400 - 150
= 250 grams
Therefore the answer is 250 grams.
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Why might squaring a number and taking the square root of a number be thought of as opposite operations?
Therefore , squaring a number and taking the square root of a number is an opposite operation as we can see in the following explanation.
How is the square root defined?A number's square root, which is the result of multiplication by itself, yields the original number. Some examples of exponents are squares and square roots. Imagine the number twenty five. Additionally, this can be expressed as expression of 5x5.
Here,
In order to square an integer, you must multiply it by itself.
The opposite of squaring a number is the act of getting the square root.
Calculating the side length of a square whose area is a certain number can be compared to finding the square root of that number.
For example: √25= √5*5 = 5
where as square of 5 : 5*5 = 25
Therefore , squaring a number and taking the square root of a number is an opposite operation as we can see in the following explanation.
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If the m<2 = 58° and the m<13 = 111°, find the measures of angles 1, 5, 8, 14, 18.
Note: x || m and z || y
Answer:
Angle 1: 58°
Angle 5: 58°
Angle 8: 111°
Angle 14: 111°
Angle 18: 58°
Step-by-step explanation:
Is there algebra in 7th grade?
Answer:
probably simple basic algebra
Step-by-step explanation:
The diameter of the circle below is 62 cm. Work out the radius of the circle. cm 62 cm
Answer: 31 cm
The radius of a 62 cm circle is 31 cm because the radius of a circle is half of the diameter.
D=diameter
R=radius
D=R2
R=D/2
Answer:
[tex]R = 31[/tex][tex]cm[/tex]
Step-by-step explanation:
[tex]D = 62[/tex]
[tex]R=\frac{D}{2} \\R=\frac{62}{2} \\R=31[/tex][tex]cm\\[/tex]
Simplify the expression the quantity 9 times x to the fourth power end quantity to the one-half power.
9 times x to the power of nine-halves
3 times x to the power of nine-halves
9x2
3x2
The solution is Option D.
The value of the equation A = ( 9x⁴ )^1/2 is A = 3x²
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = quantity 9 times x to the fourth power end quantity to the one-half power
On simplifying the expression , we get
Quantity 9 times x to the fourth power = 9x⁴
Quantity 9 times x to the fourth power end quantity to the one-half power is written as = ( 9x⁴ )^1/2
On further simplification , we get
A = ( 9x⁴ )^1/2
A = √9x⁴
Taking the square root of the value of A , we get
The value of A = 3x²
Therefore , the value of is 3x²
Hence , The value of the equation is A = 3x²
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Is there a series of rigid transformations that could map aqrs to aabc? if so, which transformations could be used?.
Yes, ΔQRS can be translate to so that Q is mapped to point A, then reflect across line containing QS.
we have two triangles ΔQRS and ΔABC in which we have ,
QR=AB = 16 cm
RS=BC= 24 cm
∠R=∠B=90°
By SAS postulate of congruence , ΔQRS ≅ ΔABC.
There are three main rigid transformations which produces congruent images.
1) Translations 2) Rotation 3) Reflection
When we look the given picture, it can be seen that ΔABC is the mirror image of ΔQRS.
But line QS is at some distance from AC , so we first translate ΔQRS to so that Q is mapped to point A, then reflect across line containing QS.
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PLEASE HELLLLPPPPP IM SO CONFUSED
What is the sample variance of the following numbers 6 4 2 7 1?
6.50 is the sample variance of the following numbers.
How to interpret a standard deviation?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.
Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
X = ∑x/n
= 3 + 4 + 2 + 7 + 1/5
= 20/5 = 4
s² = [∑(Xi - x)²/N-1]
= (6-4)² + ( 4 - 4 )²+ ( 4 - 4 )² + ( 7 - 4 )² + ( 1 - 4 )²/5 - 1
= 26/4
= 6.50
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How do you divide whole numbers step by step?
Divide the dividend's leading digit by the divisor. Divide the first two digits of the dividend by the divisor, and so on, if the divisor is greater than the dividend's first digit.
Step 2: Type the dividend's quotient above it.
what is divide?divide into parts; be divided into parts. cause one to disagree with .a significant difference between two groups that usually results in antagonism or conflict. the act or process of dividing; the condition of being divided; the act, process, or occurrence of distributing among many: distribution. : one of the segments or groups into which a whole is divided or is subdivided.
Divide the dividend's leading digit by the divisor. Divide the first two digits of the dividend by the divisor, and so on, if the divisor is greater than the dividend's first digit.
Step 2: Type the dividend's quotient above it.
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For the complex number z = negative startfraction startroot 21 endroot over 2 endfraction minus startfraction startroot 7 endroot over 2 endfraction i, what is arg(z)?.
Answer:
arg(z) = 7π/6
Step-by-step explanation:
You want the argument of the complex number -√21/2 -√7/2i.
ArgumentThe argument of the complex number is the angle it makes with respect to the positive real axis. It can be found using the arctangent function, paying attention to quadrant.
The number can be written as ...
[tex]z=-\dfrac{\sqrt{21}}{2}-\dfrac{\sqrt{7}}{2}i=\dfrac{\sqrt{7}}{2}(-\sqrt{3}-i)\\\\\arg{(z)}=\arctan{\dfrac{-1}{-\sqrt{3}}}\\\\\boxed{\arg{(z)}=\dfrac{7\pi}{6}}[/tex]
Answer: B. 210°
Step-by-step explanation:
I need the slope answers for the sheet and the regular answer
Answer:
(1.5, -3)
Step-by-step explanation:
Both equations are in slope intercept form which means that:
for y = mx + b
m = slope
b = y-intercept
The slope can help us go from the y-intercept to the next point on the graph to make the line
For the equation
y = 2x - 6
the y-intercept is -6, so plot a point there.
The slope is 2 which means you will go up 2 then to the right by 1 to the next point on the graph.
Use the same process to find the line for y = -4x + 3, but you have to keep in mind that when the "m" value is negative, that means the line will point to the left of the graph instead of the right.
Once the lines are draw, the point where they intercept will be the solution.
3/8 divided by 2/5 in fraction form and simplest form
Answer:
Step-by-step explanation:
for double fractions, invert the bottom one and then multiply them
[tex]\frac{3}{8}[/tex] * [tex]\frac{5}{2}[/tex]
= [tex]\frac{15}{16}[/tex]
= 0.9375
Triangles RST and XYZ are drawn below. If RS= 6, ST=14, XY = 9, YZ=21, and ZSZY, is ARST similar to AXYZ? Justify your answer.
Answer:
yes, ∆RST ~ ∆XYZ
Step-by-step explanation:
You want to know if ∆RST is similar to ∆XYZ when RS=6, ST=14, XY=9, YZ=21 and ∠S≅∠Y.
SAS similarityTwo triangles are similar by the SAS theorem if corresponding sides have the same ratio, and the angles between them are congruent.
ApplicationCorresponding sides are ...
RS : XY = 6 : 9 = 2 : 3
ST : YZ = 14 : 21 = 2 : 3 . . . . same ratio
The angles between them are ...
∠S, ∠Y . . . . . given as congruent
Corresponding sides have the same ratios, and the angles between them are congruent, so the triangles are similar.
What is the range of f/x )= sin x the set of all real numbers?
On solving the provided question we can say that - The Range of the given function, f(x) = sin(x) , Range = [tex]-1 < y < 1[/tex]
What is Range?Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.
The Range of the given function, f(x) = sin(x)
[tex]-1 < y < 1[/tex]
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What is set grade 3 math?
Set grade 3 math is a subject that helps children to develop a fundamental understanding of mathematics.
What is grade?Grade is a measure of academic progress. It is typically expressed as a letter or numerical score that reflects the level of achievement in a course or program. Grade is an important factor for measuring student performance and can be used to make decisions about placement, academic standing, and course selection. Grade is also used to inform students and parents about how well students are doing in their studies. Grade is often the most important factor in determining a student's overall academic success.
Set grade 3 maths covers topics such as addition, subtraction, multiplication, division, fractions, decimals, shapes, measurement, and problem-solving. This subject is important for the development of a child's critical thinking and reasoning skills. It encourages students to think logically, observe patterns, and use math operations to solve problems. Set grade 3 math also provides students with the opportunity to learn important mathematical concepts in a fun and engaging way.
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Answer:
Set grade math is a mathematical model for a collection of different things a set contains elements or members which can be mathematical objects of any kind numbers and symbols points in space.
What is the quotient of these fractions in lowest terms 3/10 2 4 ___ *?
3/5 is the quotient of these fractions in lowest form when 3/10 divides by 2/4
How to divide fractions?When two fractions are divided, the first fraction is multiplied by the second fraction's reciprocal. Finding the reciprocal of the second fraction and this can be obtained by reversing its numerator and denominator—is and then dividing the fractions. Multiply the two numerators after that. Multiply the two denominators after that, After that we need to simplify the fraction to its lowest form.
so in order to find quotient when 3/10 is divided by 2/4 we get:
quotient = (3/10) / (2/4)
=> (3/10) * (4/2)
=> 12/20
so the quotient of this division is 12/20
now we have to find the lowest form of quotient
so gcd(12,20) = 4
where gcd is greatest common divisor
so lowest form of 12/24 = (12/4) / (20/4)
=> 3 /5
so lowest form of the quotient is 3/5
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If m/RXU = 52°, then what is m/SXU?
2
X
UA
The measure of angle SXU is m ∠SXU = 128°.
What is linear angles?
If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as supplementary angles. Angles that share a vertex are said to be adjacent.
Given: m ∠RXU = 52°
We have to find the measure of angle m ∠SXU.
Let RS and VW are two lines intersects by a transversal TU.
∠3 and ∠4 are adjacent to each other after the intersection of the two lines.
Since the sum of angles of a linear pair is always equal to 180°.
⇒ ∠3 + ∠4 = 180°
52° + ∠4 = 180°
∠4 = 180° - 52°
∠4 = 128°
Hence, the measure of angle SXU is m ∠SXU = 128°.
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Simplify: (-8) x (6)-(5)x(-2)
Answer: Answer -38
Simplified version: -48 + 10
Step-by-step explanation: Sorry If I'm wrong.
FILL IN THE BLANK. the area under the normal curve to the right of muμ equals _______.
Answer: One by two
Step-by-step explanation:
Because the mu is half or 0.5, so the word in the blank will be one by two!
It is 1.4 kilometers from Jim’s house to his grandmother’s house. How far does Jim walk going to and from his grandmothers house once every day for 5 days?
Jim has to walk 7 km going to his grandmother's house once per day for 5 days.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers.
Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the data given in the question,
Distance between Jim and his grandmother's house = 1.4 km.
Jim travels once to his grandmother's house every day then,
Total distance traveled by him = 5 × 1.4 km = 7 km.
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Which expressions are equivalent to the one below? Check all that apply.
4^3 x 4^x
Answer:
d
Step-by-step explanation:
[tex]{4}^{3} . {4}^{x} [/tex]
In the following we make multiple not sum to the power
a data set was graphed using a scatterplot. the correlation coefficient, r, is 0.813. which of the following statements explains how the correlation is affected? a.) it is not affected. b.) it is affected by an influential point. c.) it is affected by inappropriate grouping. d.) it is affected by non-linearity.
The correlation coefficient is increasing, which may have an effect on the influential points. Thus, option (a) is correct.
The correlation coefficient, in general, quantifies the strength of the association between two variables.
To find non-linearity, influential spots, or improper grouping in a dataset, for example. A scatter plot is used to graph the data set.
Here, the correlation coefficient is r = 0.813.
Linearity is evident since there is a significant link between the two variables. As a result, non-linearity has no effect on it. It is not influenced by incorrect categorization when it appears that type of case correlation may be lower.
The correlation coefficient is increasing, which may have an effect on the influential points.
Thus, option (a) is correct.
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If Jasper makes 90 sandwiches, how many ounces of peanut butter will he have left?
Answer:
10
Step-by-step explanation:
each 10 peanut butter sandwiches takes 10 ounces
Answer:
10
Step-by-step explanation:
to guarantee that cans of soda are properly filled, some cans are sampled and the amounts measured. the overall average for the samples is 12 ounces. each sample contains 10 cans. the average range is 0.4 ounces. the lower control chart limit for the sample averages would be
Energy sources that are non renewable include coal, natural gas, oil, and nuclear power.
What is Nonrenewable Resources?Since we currently rely on these resources to meet the majority of our energy needs, their exhaustion and inability to be replenished poses a serious issue for humanity.Human society depends on both nonrenewable and renewable resources for its everyday energy needs. Renewable resources can naturally replenish themselves, but nonrenewable resources cannot. This is the main distinction between these two types of resources. Due to their finite availability, nonrenewable resources cannot be used responsibly.Nuclear energy, coal, natural gas, and oil are the four main categories of nonrenewable resources. Fossil fuels refer to the three fuels that make up coal, natural gas, and oil. The name "fossil" comes from the fact that fossil fuels were created deep inside the Earth over the course of millions of years from decomposing plants and animals. They are discovered in the silt and rock layers below the earth's surface. Crude oil, also known as petroleum, coal, and natural gas were produced by the pressure and heat combined with the remains of plants and animals.The Complete Question is Nonrenewable Resources.
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How do you draw a linear inequality?
To draw a linear inequality in graph the steps are mentioned below.
What are the steps to graphing an inequality?The graph of a two-variable inequality is the set of points that describe all solutions to the inequality. The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.
Steps are described below:
Step 1: Always begin by separating the variable y from the inequality's left side.
Step 2: Replace the symbol for inequality with that for equality.
Step 3: In the xy plane, graph the boundary line from step 2. You are creating the boundary line that would divide or cut the xy-plane into two sections in this stage.
Step 4: Shading one side or area of the boundary line is the final step.
Step 5: Use this optional step to check or confirm that you have shaded the boundary line's side appropriately.
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How do you know if it's greater than or less than on a graph?
To determine whether an inequality represents a relationship of "greater than" or "less than" by looking at a graph, you can look at the direction of the solid line. If the line is pointing upwards towards the right, it represents a "greater than" relationship. If the line is pointing downwards towards the right, it represents a "less than" relationship.
For example, consider the graph of the inequality "y > x + 2." The points on the graph that satisfy this inequality are those that are above the line "y = x + 2." This line represents the values of y that are equal to x + 2. The points above the line are greater than the values on the line, so the inequality "y > x + 2" represents a "greater than" relationship.
On the other hand, consider the graph of the inequality "y < x + 2." The points on the graph that satisfy this inequality are those that are below the line "y = x + 2." This line represents the values of y that are equal to x + 2. The points below the line are less than the values on the line, so the inequality "y < x + 2" represents a "less than" relationship.
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Aaron estimated that 148% of 333 is 495. is his estimate reasonable?
a. no, because his calculation should be 140% of 340.
b. no, because his calculation should be 150% of 340.
c. yes, because his calculation should be 140% of 330.
d. yes, because his calculation should be 150% of 330.
Yes, His computation should be 150% of 330, thus his estimate is accurate. So option D is true.
By dividing the desired value by the entire value and multiplying by 100, the percentage may be computed.
Example:
Required percentage value = a
total value = b
Percentage = [tex]\dfrac{a}{b} \times 100[/tex]
We have,
Aaron estimated the value, of 148% of 333 is 495.
This can be written as,
[tex]\dfrac{148}{100} \times 333[/tex]
[tex]= 492.84[/tex]
[tex]= 493\\\\[/tex]
Estimating the number, this should be equal to the,
148% ≈ 150%
333 ≈ 330
So it is equal to,
150% of 330
This can be written as,
[tex]\dfrac{150}{100} \times 330[/tex]
[tex]= 495[/tex]
Therefore, his estimate is reasonable because his calculation should be 150% of 330. So option D is true.
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Luisa began walking up a hill at a spot where the elevation is 0.9 km. After she walked
3 km, she saw a sign giving the elevation as 0.95 km. How far will she have walked when she
reaches and elevation of 1.1 km?
Answer:
3.82 km
Step-by-step explanation:
Assuming that the change in elevation is linear, we can calculate the elevation change per km traveled. The known values are the start (0km) and the sign (3km). The elevation gain over that interval is (0.95-9.0)km = 0.5km. That was for an distance interval of 3km, so we can write:
(0.5km elevation gain)/(3km distance)
We can use this as a rate change and and use it in a linear equation to predict the elevation as a function of distance.
Let y be the elevation and x the distance, both in km.
y = (0.183)(x)+b, where b is the elevation at the start of the trail. We can find b by using this equation and entering one of the two data points. Lets use the elevation of 0.95m at 3km distance:
y = (0.183)(x)+b
0.95 = (0.183)(3)+b
b = 0.4km
The full equation is :
y = (0.1833)X + 0.4
Enter 1.1 km for y and calculate x, the distance to reach 1.1 km altitude.
1.1 = (0.1833)X + 0.4
X = 3.82 km