Step-by-step explanation:
If [tex]mKg[/tex] of mass is placed on spring with spring constant [tex]k[/tex],
[tex]mg=kx[/tex]
where [tex]g[/tex] is universal gravitational constant
[tex]x[/tex] is the displacement in the spring.
In case 1:
[tex]25g=k(0.15)\\k=\frac{25g}{0.15}[/tex]
In case 2:
[tex]mg=k(0.23)[/tex]
Using result from case 1,
[tex]mg=\frac{25g}{0.15}\times 0.23[/tex]
[tex]m=[/tex][tex]38.33Kg[/tex]
How many solutions does this system of equations have?
exactly one
exactly two
infinitely many
none
Answer:
exactly one
Step-by-step explanation:
1. subtract 2x from the equation 2x + y = 1
2. now you should have y= -2x + 1
3. then on the second equation subtract 4x from 4x + 2y = 2
4. now you should have 2y = -4x + 2
5. divide everything by 2
6. now you should have y = -2x + 1
7. since you got an exact answer on both of them then it is exactly one
Determine whether the following statements are true or false. If false, explain why.
1) Point (3,2) to (3,-2) is a reflection over the y-axis.
2) A(1,3) to A'(-1,3) is a reflection over the y-axis
Answer:
see the explanation
Step-by-step explanation:
we know that
The rule of the reflection of a point across the y-axis is equal to
(x,y) -----> (-x,y)
The rule of the reflection of a point across the x-axis is equal to
(x,y) -----> (x,-y)
so
Verify each statement
1) Point (3,2) to (3,-2) is a reflection over the y-axis.
The statement is false
Because, is a reflection over the x-axis
A reflection over the y-axis will be
(3,2) -----> (-3,2)
2) A(1,3) to A'(-1,3) is a reflection over the y-axis
The statement is true
SOS PLEASE HELP so I don't fail math
Answer:
2 years ago :/
Step-by-step explanation:
help, succession formula
Answer:
[tex]a_n=-3*\left ( -\frac{2}{3} \right )^n \ n>=0[/tex]
Step-by-step explanation:
Succession can be understood as a sorted collection of values that respond to a general term or rule. We need to find if these numbers are in arithmetic progression or geometric progression.
In an arithmetic progression, every number is obtained as the previous number plus or minus a constant value called common difference. In a geometric progression, we get the next numbers as the previous one multiplied or divided by a constant value, called the common ratio.
If we try to find a possible common difference between first and second terms we get:
[tex]2-(-3)=5[/tex]
If it was an arithmetic progression, third term should be
[tex]2+5=7[/tex]
Which is obviously not true. Now let's try to find a possible common ratio by dividing second by first term
[tex]r=\frac{2}{-3}=-\frac{2}{3}[/tex]
Testing our value to find the third term we get
[tex]a_3=2*(-\frac{2}{3})=-\frac{4}{3}[/tex]
Since we have more terms to test:
[tex]a_3=(-\frac{4}{3})*(-\frac{2}{3})=\frac{8}{9}[/tex]
The given value is just as predicted
The fourth term can be accurately predicted also:
[tex]a_4=(\frac{8}{9})*(-\frac{2}{3})=\frac{16}{27}[/tex]
Now we are sure it's a geometric progression, it can easily be stated the general term of the progression is
[tex]a_n=a_1*r^n \ n>=0[/tex]
[tex]a_n=-3*\left ( -\frac{2}{3} \right )^n \ n>=0[/tex]
3. In order to enter the state fair, there is
an admission cost. Each game is $3.
Steven went to the state fair, played
4 games and spent a total of $20 on
admission and games. Assume the
relationship is linear. Find and interpret
the rate of change and the initial value.
Answer:
C = 8 + 3x
The rate of change in the above equation is 3 dollars per game and it interpret the cost per game.
The initial value in the above equation is 8 dollars, which interpret the entry fee that every one person has to pay to enter the fair.
Step-by-step explanation:
Let the admission cost of the fair is $x and each game is $3.
Now, Steven went to the state fair, played 4 games and spent a total of $20 on admission and games.
So, we can write 20 = x + 4 × 3 {As the relation is linear}
⇒ x = $8
Therefore, the admission cost in the fair is $8.
Therefore, the equation that models the situation is
C = 8 + 3x ............ (1)
Where C is the total cost and x is the number of games played.
So, the rate of change in equation (1) is 3 dollars per game and it interprets the cost per game.
Again, the initial value in equation (1) is 8 dollars, which interprets the entry fee that each person has to pay to enter the fair. (Answer)
A class of 32 consists of students who either have red or yellow shirts if there are 12 more people with red shirts in there are people with yellow shirt many students have red shirt
Answer:
22 people with red shirts and 10 people with yellow shirts
What are some math equations that end up making the answer being 209
Answer:
Step-by-step explanation:
(0^209 + 1(209)/(209))^0 + 208
Evaluate the expression –0.4(3x – 2) + StartFraction 2 x plus 4 Over 3 EndFraction for x = 4
Answer:
[tex]-0.4(3x-2)+\frac{2x+4}{3}=0\ \textrm{for}\ x=4[/tex]
Step-by-step explanation:
Given:
The expression to evaluate is given as:
[tex]-0.4(3x-2)+\frac{2x+4}{3}[/tex]
The value of 'x' is 4.
Plug in 4 for 'x' in the above expression and simplify. This gives,
[tex]=-0.4(3(4)-2)+\frac{2(4)+4}{3}\\=-0.4(12-2)+\frac{8+4}{3}\\=-0.4(10)+\frac{12}{3}\\=-4+4\\=0[/tex]
Therefore, the value of the given expression for 'x' equal to 4 is 0.
The required value of the given expression is 0 when substituting the value of x = 4 into the expression.
The expression is given as follows:
-0.4(3x - 2) + (2x + 4) / 3
Let's evaluate the given expression for x = 4:
Expression = -0.4(3x - 2) + (2x + 4) / 3
Substitute x = 4 into the given expression:
Expression = -0.4(3 × 4 - 2) + (2 × 4 + 4) / 3
Expression = -0.4(12 - 2) + (8 + 4) / 3
Expression = -0.4(10) + 12 / 3
Expression = -4 + 12 / 3
Expression = -4 + 4
Expression = 0
Therefore, when x = 4, the value of the expression is 0.
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Make b the subject of the formula
[tex]a = \sqrt{b + 6} [/tex]
Answer:
a^2 -6
Step-by-step explanation:
use ur basic knowing of equations
Assume that µ = 500 and s = 100. Your study shows a sample of size 22 with a mean of 530 and standard deviation of 113. a. What is the most powerful test to use to test the hypothesis that the mean of the sample was drawn from the above Null Hypothesis Population? b. What is the value of the test statistic? c. What do you conclude using a = 0.052 tail?
Answer: using t - test value is 1.37<2.08( At 0.05 level of significance)
The mean of the sample was drawn from the population.
Step-by-step explanation:
Here sample size n=22
Given sample mean =530
Given population mean =500
[tex]t=\frac{sample mean-µ}{\frac{S}{\sqrt{n-1} } }[/tex]
given sample standard deviation s=100
a) null hypothesis:- The mean of the sample was drawn from the population µ =500
Alternative hypothesis:-
The most powerful test you can use is t - distribution.
The test statistic is
[tex]t=\frac{sample mean- µ}{\frac{S}{\sqrt{n-1} } }
here S is the standard deviation of the sample
b) The value of the test statistic
[tex]t=\frac{sample mean- µ}{\frac{S}{\sqrt{n-1} } }
substitute given values sample size n=22
sample mean =530
sample standard deviation s =100
mean of the population µ =500
the calculated value of t =[tex]\frac{530-500}{\frac{100}{\sqrt{22} } }[/tex]
the calculated value=1.3748
c) The degrees of freedom =n-1 = 22-1 = 21
The table value of t are 0.05 level of significance with 21 degrees of freedom is 2.08
The calculated value 1.37<2.08
∴ we accept null hypothesis at 0.05 level of significance
conclusion:-
The mean of the sample was drawn from the population.
A t-test is the most powerful test for this hypothesis. The test statistic value is calculated using t = (X - µ) / (s / √n). Based on a significance level of 0.05, we can conclude by comparing the calculated t-value with the critical t-value from t-distribution table.
Explanation:The subjects of this question are hypothesis testing and statistics.
To answer your question: a) The most powerful test to use to test your hypothesis is the t-test for single mean. This is because you have one sample mean, one hypothesized population mean, and the population standard deviation is not known.
b) The value of the test statistic can be calculated using the formula: t = (X - µ) / (s / √n), where X is the sample mean, µ is the population mean, s is the sample standard deviation, and n is the sample size. Plugging in your values, the formula becomes t = (530 - 500) / (113/ √22).
c) With a = 0.05, we conclude by comparing the calculated t-value with t-distribution table (df = 22-1 = 21). If the calculated t-value exceeds the critical t-value from the t-distribution table, we reject the null hypothesis.
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Triangle DEF (not shown) is similar to ABC shown, with angle B congruent to angle E and angle C congruent to angle F. The length of side DE is 6 cm. If the area of ABC is 5 square centimeters, what is the area of DEF ?
Answer:
Area of ΔDEF is [tex]45\ cm^2[/tex].
Step-by-step explanation:
Given;
ΔABC and ΔDEF is similar and ∠B ≅ ∠E.
Length of AB = [tex]2\ cm[/tex] and
Length of DE = [tex]6\ cm[/tex]
Area of ΔABC = [tex]5\ cm^2[/tex]
Solution,
Since, ΔABC and ΔDEF is similar and ∠B ≅ ∠E.
Therefore,
[tex]\frac{Area\ of\ triangle\ 1}{Area\ of\ triangle\ 2} =\frac{AB^2}{DE^2}[/tex]
Where triangle 1 and triangle 2 is ΔABC and ΔDEF respectively.
If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.
[tex]\frac{5}{Area\ of\ triangle\ 2} =\frac{2^2}{6^2}\\ \frac{5}{Area\ of\ triangle\ 2}=\frac{4}{36}\\ Area\ of\ triangle\ 2=\frac{5\times36}{4} =5\times9=45\ cm^2[/tex]
Thus the area of ΔDEF is [tex]45\ cm^2[/tex].
The horizontal line segment at the top of the polygon on the grid below is how many units long?
Answer:
6 units long.
Step-by-step explanation:
Given:
A polygon drawn on a graph.
In order to determine the distance of the horizontal line at the top, we find the coordinates of the end points and then use distance formula to find the exact distance.
Let us label the polygon as ABCD as shown below. AB is the length of the horizontal line.
Coordinates of A are [tex](x_1,y_1)=(-3, 4)[/tex] as seen in the graph.
Coordinates of B are [tex](x_2,y_2)=( 3, 4)[/tex] as seen in the graph.
Now, distance formula for two points [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex] is:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d_{AB}=\sqrt{(3-(-3))^2+(4-4)^2}\\d_{AB}=\sqrt{(3+3)^2+0}\\d_{AB}=\sqrt{36}=6\ units[/tex]
Therefore, the horizontal line at the top is 6 units long.
Answer:
6 units long
Step-by-step explanation:
brainly patrol what is wrong with that
what is the simplified expression to 3.4m+2.4m
Final answer:
The simplified expression for 3.4m + 2.4m is 5.8m. You simply add the coefficients of like terms.
Explanation:
To simplify the expression 3.4m + 2.4m, we need to combine like terms. The term 'like terms' refers to terms that have the exact same variable raised to the same power. In this case, both terms have 'm' as the variable, and it's not raised to any power (which is the same as being raised to the power of 1).
Combine the coefficients (numerical parts) of the like terms:
3.4m + 2.4m = (3.4 + 2.4)m
Add the coefficients: 3.4 + 2.4 = 5.8
Therefore, 3.4m + 2.4m = 5.8m.
Cos(theta)= -.9041, 180degress< theta <270degress
Answer:
[tex]\theta=205.298^o[/tex]
Step-by-step explanation:
We know
[tex]cos\theta=-.9041[/tex]
in the third quadrant [tex]180^o<\theta<270^o[/tex]
We use a scientific calculator to find the inverse cosine of -0.9041 to find
[tex]\theta=154.702^o[/tex]
Since this angle is not in the required quadrant we must find the other angle who has the same cosine. The required angle is equidistant from the found value from the 180 degrees angle, so our solution is
[tex]\theta=180^o+(180^o-154.702)=205.298^o[/tex]
Following a translation, the measures of the angles in a pre-image are congruent to the measures of the corresponding angles in its image.
True
False
Find percent increase, round to the nearest percent
From 24 teachers to 225 pencils
Answer: 838% to the nearest percent
Step-by-step explanation:
225 - 24 =201
=201/24 * 100
= 838% to the nearest percent
What is the y-intercept of y = 5?
Answer:
Y- intercept is 5!
In recent year 34% of all college students were enrolled part time if 6.1 million college students were enrolled part time that year what was the total number of college students
The total number of college students was 17.94 million.
Step-by-step explanation:
Percentage of part time students = 34%
Number of part time students = 6.1 million
Let,
x be the total number of students
According to statement,
34% of x = 6.1 million
[tex]\frac{34}{100}x=6.1\ million\\0.34x=6.1[/tex]
Dividing both sides by 0.34
[tex]\frac{0.34x}{0.34}=\frac{6.1}{0.34}\\x=17.94\ million[/tex]
The total number of college students was 17.94 million.
Keywords: percentage, division
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This pair of figures is similar. Find the missing side.
Answer:
x=2
Step-by-step explanation:
so if the bigger one is 16 and the other one is 4 that means you need to multiply 4 by 4 to get 16 so to find x you need to divide the 8 by 4 to find your answer
Answer:
x = 2
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{x}{8}[/tex] = [tex]\frac{4}{16}[/tex] ( cross- multiply )
16x = 32 ( divide both sides by 16 )
x = 2
• What ratio is equivalent to 6 to 2? Complete the statement.
)) The ratio 6 to 2 is equivalent to the ratio
to ?
3 to 1
The ratio 6 to 2 is equivalent to the ratio 3 to 1, obtained by dividing both the numerator and denominator of the ratio by their greatest common divisor, which is 2.
Explanation:To find a ratio equivalent to 6 to 2, you simplify the ratio by dividing both numbers by their greatest common factor. In this case, the greatest common factor is 2, so 6 ÷ 2 = 3 and 2 ÷ 2 = 1. Therefore, the equivalent ratio is 3 to 1.
The ratio 6 to 2 can be simplified by dividing both numbers by their greatest common divisor, which is 2. Therefore, 6 divided by 2 is 3, and 2 divided by 2 is 1. This simplification shows that the ratio 6 to 2 is equivalent to 3 to 1. Ratios compare two quantities and can be expressed in several forms such as fractions, with a colon, or using the word "to". An equivalent ratio maintains the same proportional relationship between its components, just like how 6:2 has the same proportional relationship as 3:1.
find the slope between the points (-4,5) and (-8,-5)
Answer:
[tex] \frac{5}{2} \\ [/tex]
Step-by-step explanation:
[tex] \frac{ - 5 - 5}{ - 8 - - 4} [/tex]
Y - Y divided by X - X, the Y is 5 and the X is 2 (Rise over Run)
Answer:
[tex]\displaystyle 2\frac{1}{2} = m[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-5 - 5}{4 - 8} = \frac{-10}{-4} = 2\frac{1}{2}[/tex]
I am joyous to assist you anytime.
A rectangle has an area of 24 sq. inches and a perimeter of 50 in. what are the dimensions of the rectangle
Final answer:
To find the dimensions of a rectangle with an area of 24 sq. inches and a perimeter of 50 inches, we set up a system of linear equations and solve for the length and width. The dimensions are found to be either 24 inches by 1 inch or 1 inch by 24 inches.
Explanation:
The question given by a student involves finding the dimensions of a rectangle given its area and perimeter. Given the area (24 sq. inches) and the perimeter (50 in.), we can set up two equations to solve for the length and width:
Area = length imes width = 24 sq. inches
Perimeter = 2 imes (length + width) = 50 inches
We can divide the perimeter by 2 to get the sum of the length and width:
25 = length + width
Since we have two equations, this forms a system of linear equations which we can solve simultaneously. First, assume the length is the larger dimension and let us represent it by 'L' and the width by 'W'. We have:
L imes W = 24
L + W = 25
To solve for L and W, we can use substitution or elimination methods. Let's assume we solve for W in terms of L using the first equation, W = 24/L, and then we substitute it into the second equation:
L + 24/L = 25
Multiplying both sides by L to clear the fraction, we get:
L² + 24 = 25L
Then we rearrange the terms to set the equation to zero:
L² - 25L + 24 = 0
Now we can factor this quadratic equation to find the values of L:
(L - 1)(L - 24) = 0
So, L can be either 1 inch or 24 inches. If L is 24 inches, then W will be 1 inch (since 24 imes 1 = 24), and if L is 1 inch, then W will be 24 inches. Either way, the dimensions that satisfy both the area and perimeter equations are 24 inches by 1 inch.
The dimensions of the rectangle are [tex]\( {24 \text{ inches} \text{ by } 1 \text{ inch}} \)[/tex].
To find the dimensions of the rectangle, let's denote the length by l and the width by w.
Given:
1. The area of the rectangle is 24 square inches:
[tex]\[ l \cdot w = 24 \][/tex]
2. The perimeter of the rectangle is 50 inches, which gives us the equation:
[tex]\[ 2l + 2w = 50 \][/tex]
Let's solve these equations step by step.
From the perimeter equation:
[tex]\[ 2l + 2w = 50 \][/tex]
Divide the entire equation by 2 to simplify:
[tex]\[ l + w = 25 \][/tex]
Now we have two equations:
[tex]\[ l + w = 25 \]\[ l \cdot w = 24 \][/tex]
Let's solve for l and w using substitution or elimination.
From ( l + w = 25 ), we can express l as:
[tex]\[ l = 25 - w \][/tex]
Substitute [tex]\( l = 25 - w \)[/tex] into [tex]\( l \cdot w = 24 \)[/tex]:
[tex]\[ (25 - w) \cdot w = 24 \][/tex]
Expand and rearrange the equation:
[tex]\[ 25w - w^2 = 24 \]\[ w^2 - 25w + 24 = 0 \][/tex]
Now, solve this quadratic equation using the quadratic formula [tex]\( w = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \)[/tex], where ( a = 1 ), ( b = -25 ), and ( c = 24 ):
[tex]\[ w = \frac{{-(-25) \pm \sqrt{{(-25)^2 - 4 \cdot 1 \cdot 24}}}}{{2 \cdot 1}} \]\[ w = \frac{{25 \pm \sqrt{{625 - 96}}}}{2} \]\[ w = \frac{{25 \pm \sqrt{{529}}}}{2} \]\[ w = \frac{{25 \pm 23}}{2} \][/tex]
So, we get two possible values for w:
[tex]\[ w = \frac{{25 + 23}}{2} = 24 \]\[ w = \frac{{25 - 23}}{2} = 1 \][/tex]
Now, find l for each value of w:
1. If ( w = 24 ):
[tex]\[ l = 25 - 24 = 1 \][/tex]
2. If ( w = 1 ):
[tex]\[ l = 25 - 1 = 24 \][/tex]
What is the first step to take when solving this linear system of equations by the addition-subtraction method? 2x + 4y = 3 x + 3y =13 A) solve for y in terms of x B) solve for x in terms of y C) multiply the first equation by −2 D) multiply the second equation by −2
The right answer is Option D.
Step-by-step explanation:
Given equations are;
2x+4y=3 Eqn 1
x+3y=13 Eqn 2
When we use subtraction-addition method, we make one of the variables same with opposite signs so that only one variable remains after addition or subtraction.
In the given problem, we will multiply Eqn 2 with "-2" so that the x variables become equal and then we can add both the equations and solve for y.
Therefore,
The first step will be to multiply the second equation by -2 to solve the linear system of equations.
The right answer is Option D.
Keywords: linear equations, subtraction
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Answer:
It's D.
Step-by-step explanation:
It was correct on my unit test review.
The ____ value of a digit is based on its location.
Answer:
place
Step-by-step explanation:
Answer:
The answer is " Place value"
Step-by-step explanation:
The place value determines the value of the digit in a number, based on its position.
A standard form number is divided into groups of three digits using commad. Each of these groups is called a period.
A beauty salon buys bottles of styling gel for 4.50 per bottle and marks up the price by 40% By how much does the price go up.
Answer:
It goes up my $1.80
Step-by-step explanation:
You multiply $4.50 by 0.40 and you get 1.80 and that’s how much it goes up by
What is 7225 / 8 with the remainder as a whole number
Answer:
903 1/8
Step-by-step explanation:
Just divide 7225 by 8. :) I put it in fraction form but decimal form is just 903.125. I hope this helps you out. :)
Answer:
its 903 with 1 left over
I need help with this math problem.
===============================================
Explanation:
The x intercept is (-2,0) which is where the graph crosses the x axis.
The y intercept is (0,-6) which is where the graph crosses the y axis.
-----
Find the slope of the line through those two points
m = (y2-y1)/(x2-x1)
m = (-6-0)/(0-(-2))
m = (-6-0)/(0+2)
m = -6/2
m = -3
-----
The y intercept (0,-6) leads to b = -6
Both m = -3 and b = -6 plug into y = mx+b to get
y = mx+b
y = -3x+(-6)
y = -3x-6
-----
Now add 3x to both sides
y = -3x-6
y+3x = -3x-6+3x
3x+y = -6
-----
Lastly, multiply both sides by -2 so that the "-6" on the right hand side turns into "12" (each answer choice has 12 on the right hand side)
3x+y = -6
-2(3x+y) = -2(-6)
-2(3x)-2(y) = 12
-6x-2y = 12
which is what choice B shows.
Georgia's baby brother weighed less than 11 pounds when he was born. Which of the following could be the number of ounces Georgia's baby brother weighed? Select two that apply.
A
156 ounces
B
170 ounces
C
186 ounces
D
190 ounces
Answer:
Step-by-step explanation:
B :because 11 pound in Ounces is 176
Which expression is equivalent to
First choice: m^32n^16
Hope this helps!
Answer:
The correct answer would be m^32n^16.
Step-by-step explanation:
This is because when you have a power inside parenthesis multiplied by a power outside the parenthesis, you are simply going to multiply the numbers like so:
8 • 4 = 32
4 • 4 = 16
m^32n^16
Hope this helps,
♥A.W.E.S.W.A.N.♥
A bag contains purple marbles and white marbles, 34 in total. The number of purple marbles is 1 less than 4 times the number of white marbles. How many purple marbles are there?
There are 27 purple marbles
Step-by-step explanation:
Let p be the purple marbles
and
w be the white marbles
Then according to given statements
[tex]p+w = 34\ \ \ Eqn\ 1\\p = 4w-1\ \ \ Eqn 2[/tex]
Putting p = 4w-1 in equation 1
[tex]4w-1 +w = 34[/tex]
Adding one on both sides
[tex]5w-1+1 = 34+1\\5w = 35[/tex]
Dividing both sides by 5
[tex]\frac{5w}{5} = \frac{35}{5}\\w = 7[/tex]
Putting w = 7 in equation 2
[tex]p = 4(7)-1\\p = 28-1\\p = 27[/tex]
Hence,
There are 27 purple marbles
Keywords: Linear equation
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