Answer:
The exact value of x is 2.Step-by-step explanation:
To find the exact value of x, we need to solve the given equation for x. The equation is:
32^1/25 x 2^x = 8^1/4
To solve this equation, we need to rewrite it in a form that allows us to isolate the variable x. We can start by using the properties of exponents to simplify the left-hand side of the equation. We can use the property that says that raising a number to a fractional power is the same as taking the square root of that number, raised to the power of the denominator of the fraction. So, we can write:
(32^1/25)^2 = (32^1/25)^25/25 = 32^1/25
This simplification allows us to rewrite the left-hand side of the equation as follows:
32^1/25 * 2^x = (32^1/25)^2 * 2^x
Next, we can use the property of exponents that says that the product of two numbers raised to the same power is equal to the product of the numbers, raised to that power. So, we can rewrite the left-hand side of the equation as follows:
(32 * 2)^1/25 * 2^x = (32^1/25)^2 * 2^x
Then, we can use the property of exponents that says that raising a product to a power is the same as raising each factor to that power. So, we can rewrite the left-hand side of the equation as follows:
(32^1/25) * 2^(1/25 + x) = (32^1/25)^2 * 2^x
Finally, we can use the property of exponents that says that the exponent of a power is equal to the product of the exponents of the base and the power. So, we can rewrite the left-hand side of the equation as follows:
(32^1/25) * 2^(1/25 * 25 + 1 * x) = (32^1/25)^2 * 2^x
Since the right-hand side of the equation is already in a form that allows us to isolate the variable x, we can now use the property of exponents that says that raising a number to a power and then taking the square root of that number is the same as
An equation is given.
y=3x+c
Create an equivalent equation by solving for c in terms of y and x.
An equation is given as y=3x+c, an equivalent equation can be created by by solving for c in terms of y and x as y-3x.
How can this be calculated?An equation is given as y=3x+c , the concept that can be used to find the expression of c is the subject of the formular.
It should be noted that the subject of a formula is the variable that is being worked out which is been recognised as the letter on its own on one side of the equals sign.
y=3x+c
c= y-3x
Then solving for c in terms of y and x will give us (y-3x)
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A man is four times as old as his son. In 5 year’s time he will be three times as old as his son. What is the present age of the son in years?
The age of the son is 10 years old.
Lets simplify the above problem ,
Let assume man's age = a
Let assume son's age = b
If a man is 4 times as old as his son, then
=> a= 4b
In 5 years, he will only be 3 times as old as his son, then
= a+5
= 3(b+5)
Apply substitution method :
4b+5
=3b+15
b=10
a =40
Hence the son age is 10 years old.
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a news article claims that 90% of college students believe that their online courses are as good as or superior to traditional face-to-face instruction. a statistics student disagrees with this statement and believes the true proportion of college students who believe that their online courses are as good as or superior to traditional face-to-face instruction is less than 90%. the student tests the hypotheses if the statistics student concludes that the true proportion of college students who believe that their online courses are as good as or superior to traditional face-to-face instruction is 90%, when in fact, the proportion is less than 90%, the statistics student has made which type of error?
The correct answer is the error made by the students of statistics is of Type 1 error.
As the question states that,
The news article that claim the number of student who believes that their online courses are as good as or superior to traditional face-to-face instruction = 90%.
The two types of error known are:
Type I error : Reject the null hypothesis when the null hypothesis is true.
Type II error : Fail to reject the null hypothesis, when the null hypothesis is NOT true.
From the question,
The hypothesis that the student test is H₀ : p = 0.90, Hₐ : p < 0.90 .
Here, p<0.90 means that College student disagree with the statement.
The student had rejected the null hypothesis,
and concluded that p < 0.90 , when in fact the null hypothesis is true .
The correct answer is Type 1 error.
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If y=156 when x=39 what is y when x is 17 please show work
The value of y when x = 17 based on y=156 when x=39 is 68
What is the value of y?Based on the given task content; the value of y can be determined by using ratio
y = 156 when x = 39
y = ? when x = 17
Equate the ratio of y to x
156 : 39 = y : 17
156/39 = y / 17
cross product
156 × 17 = y × 39
2,652 = 39y
divide both sides by 39
y = 2,652 / 39
= 68
In conclusion, y is 68 when x = 17 when solved with ratio.
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What is median math 7th grade?
Median is the middlemost value after the data set is sorted in ascending or descending order.
What is median?
The data set's median is the value in the middle.when we will put all the numbers in ascending or descending order, and then choose the middle number to determine the median. There will only be one middle integer if the number of data points is odd. If the number of data points is even, you must choose the middle two numbers, add them up, and divide by two. Your median will be that value.
so if we given with a data set 2, 1 ,4, 3,2 ,2 ,1
so in order to find the median of a data set we will sort it into ascending order and then find the middle most value as the number of element is odd.
so after sorting the data set is like 1 , 1 , 2 , 2, 2 , 3 , 4 so the middle value is 4 the element which is 2 and hence median of the data set is 2.
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Discrete Random Variables
A discrete random variable may take on only a countable number of distinct values such as 0,1,2,3,4,...
Discrete random variables are usually (but not necessarily) counts. If a random variable can take only a finite number of distinct values, then it must be discrete. Examples of discrete random variables include the number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor's surgery, and the number of defective light bulbs in a box of ten.
The probability distribution of a discrete random variable is a list of probabilities associated with each of its possible values. It is also sometimes called the probability function or the probability mass function.
Example'
The cumulative distribution function for the above probability distribution is calculated as follows:
The probability that [tex]X[/tex] is less than or equal to is 0.1,
the probability that [tex]X[/tex] is less than or equal to 2 is 0.1+0.3 = 0.4,
the probability that [tex]X[/tex] is less than or equal to 3 is 0.1+0.3+0.4 = 0.8, and
the probability that [tex]X[/tex] is less than or equal to 4 is 0.1+0.3+0.4+0.2 = 1.
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What is the mean value of 1234567?
The mean of the data 1,2,3,4,5,6,7 is 4.
Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
The basic formula to calculate the mean is calculated based on the given data set. Each term in the data set is considered while evaluating the mean. The general formula for mean is given by the ratio of the sum of all the terms and the total number of terms. Hence, we can say;
Mean = Sum of the Given Data/Total number of Data
Mean= 1+2+3+4+5+6+7 / 7 = 28/7 = 4
Hence, The mean of the data 1,2,3,4,5,6,7 is 4.
Complete question: What is the mean value of 1,2,3,4,5,6,7?
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What is the difference between fit Fit_transform and predict methods?
Recall that the transform() and predict() functions only operate on test data, while the fit transform() function only operates on training data.
What is difference between fit and Fit_transform?The mean and standard deviation for a particular feature are calculated using the fit(data) approach and then scaled. Scaling with mean and standard deviation determined by the. fit() method is done using the transform(data) method. The methods fit transform() and transform are both used for fits.
Predict() makes predictions based on the parameters it learned during fit on the testing examples, while the fit() method applies the model to the input training instances. Fit Transform is a mathematical expression that means to calculate, then transform (say calculating the means of columns from some data and then replacing the missing values). In order to alter the training set, you must also calculate it.
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A grab-bag contains 20 packages worth $. 70 each, 15 packages $. 60 cents each, and 5 packages worth $. 30 each. What is the expected value if you have to pay $. 50 to pick one package at random?.
The expected value to pick a package is $.1125.
To find the expected value, you need to multiply the value of each package by the probability of selecting it and then add up all of these values.
The probability of selecting one of the $.70 packages is 20/40 = 1/2, since there are a total of 40 packages and 20 of them are worth $.70. The expected value of selecting one of these packages is $.70 * (1/2) = $.35
The probability of selecting one of the $.60 packages is 15/40 = 3/8, since there are a total of 40 packages and 15 of them are worth $.60. The expected value of selecting one of these packages is $.60 * (3/8) = $.22.5
The probability of selecting one of the $.30 packages is 5/40 = 1/8, since there are a total of 40 packages and 5 of them are worth $.30. The expected value of selecting one of these packages is $.30 * (1/8) = $.0375
The expected value of selecting one package at random is therefore $.35 + $.22.5 + $.0375 = $.61.25. However, you have to pay $.50 to pick a package, so the net expected value is $.61.25 - $.50 = $.1125.
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Picking a bundle is anticipated to be worth $.1125.
You must multiply the value of each package by the likelihood that it will be chosen before adding up all of these values to arrive at the expected value.
Given that there are a total of 40 packages and 20 of them are valued at $.70 each, the likelihood of choosing one of the $.70 packages is 20/40 = 1/2. Selecting one of these packages has an expected value of $.70 * (1/2) = $.35.
Given that there are 40 products in total and 15 of them are worth $.60 each, the probability of choosing one of the $.60 packages is 15/40 = 3/8. Choosing one of these packages will result in a value of $.60 * (3/8) = $.22.5.
There are a total of 40 packets, and 5 of them are worth $.30, hence the likelihood of choosing one of the $.30 packages is 5/40 = 1/8. By choosing one of these packages, the predicted value is $.30 * (1/8) = $.0375.
Therefore, $.35 + $.22.5 + $.0375 = $.61.25 is the expected value of choosing one package at random. The net expected value is $.61.25 - $.50 = $.1125 due to the fact that you must pay $.50 to choose a bundle.
Find the coordinates of point A' if point A(7, -2) is rotated 180 about the origin
Answer:
Below
Step-by-step explanation:
See attached image below
What is the formula of asymptote?
The formula for finding the asymptote of a hyperbola is
y-k =+/- b/a( x-h)
Hyperbola
A hyperbola is an open curve with two branches, the intersection of a plane with both halves of a double cone. The plane does not have to be parallel to the axis of the cone; the hyperbola will be symmetrical in any case.
An asymptote of the curve y = f(x) or in the implicit form: f(x, y) = 0 is a straight line such that the distance between the curve and the straight line lends to zero when the points on the curve approach infinity.
In Mathematics, infinity is the concept describing something larger than the natural number. It generally refers to something without any limit. This concept is predominantly used in the field of Physics and Math which is relevant in a number of fields.
The quintessential example of asymptotes are the vertical or horizontal lines given by x=0 and y=0, respectively, relative to the graph of the real-valued function f(x)=1x f ( x ) = 1 x in the first quadrant.
In the cartesian system, the coordinate plane is divided into four equal parts by the intersection of the x-axis (the horizontal number line) and the y-axis (the vertical number line). These four regions are called quadrants because they each represent one-quarter of the whole coordinate plane.
The formula for finding the asymptote of a hyperbola is
y-k =+/- b/a( x-h)
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An asymptote of the curve y = f(x) or in the implicit form: f(x, y) = 0 is a straight line such that the distance between the curve and the straight line lends to zero when the points on the curve approach infinity.
The quintessential example of asymptotes are the vertical or horizontal lines given by x=0 and y=0, respectively, relative to the graph of the real-valued function f(x)=1x f ( x ) = 1 x in the first quadrant.
Box B has a mass of 350 grams and is 45 grams lighter than box A. What is the mass of box A?
A) 305 grams
B) 320 grams
C) 395 grams
D) 420 grams
Answer:
C) 395 grams
Step-by-step explanation:
Box B = 350g and is lighter than box A, 45 gram
Box A = Box B +45
350 + 45 = 395 grams
So, the answer is C
HELP ASAP 50 POINT QUESTION 100 POINT ASSIGNMENT!!!
An indoor staircase has a 14 inch vertical rise per step to get to the second floor of the house. If the angle of elevation is 47 degrees and there are 13 feet of horizontal space total for each of the landings combined, answer the following questions showing each step of your work:
A: What is the landing space per step (in inches, rounded to the nearest inch)?
B: Find the vertical rise from the 1st floor to the 2nd floor (in feet, rounded to the nearest foot).
(Please and thank you! I will mark brainliest to the first answer that’s correct!)
a) 7 in
b) 72 steps
Step-by-step explanation:
Angle of elevation formula:
where is the angle of elevation, y is the vertical distance (rise) and x is the horizontal distance.
a) Given:
b) Given:
1st floor = 21 feet
2nd floor = 21 feet
⇒ Total height = 21 + 21 = 42 feet
1 foot = 12 inches
⇒ 42 feet = 42 x 12 = 504 inches
Using vertical rise of 7 in per step found in part (a):
Number of steps = 504 ÷ 7 = 72
Increased accuracy
Using unrounded vertical rise of 12tan(32):
Number of steps = 504 ÷ 12tan(32) = 67 steps to the nearest step
pls help me I’m so tired
Answer:
Step-by-step explanation:
[tex]Equation 1\\y-2x=-2\\Equation 2\\8x=-3y-48[/tex]
To begin, solve equation 1 for y:
[tex]y=2x-2[/tex]
Then substitute 2x-2 for y in equation 2:
[tex]8x=-3(2x-2)-48[/tex]
Now solve for x:
[tex]8x=-3(2x-2)-48\\8x=-6x+6-48\\8x=-6x-42\\(8x)+6x=(-6x-42)+6x\\14x=-42\\\frac{14x}{14}=\frac{-42}{14}\\x=-3[/tex]
Substitute this x-value into equation 1:
[tex]y=2x-2\\y=2(-3)-2\\y=-6-2\\y=-8[/tex]
So, the ordered pair that best represents the solution to this system of equations is (-3,-8). This can be proven by substituting these values for x and y into the original equations:
[tex]y-2x=-2\\(-8)-2(-3)=-2\\-8-(-6)=-2\\-8+6=-2\\-2=-2[/tex]
and
[tex]8x=-3y-48\\8(-3)=-3(-8)-48\\-24=24-48\\-24=-24[/tex]
What is the area of a triangle with a base of 7 1/2 feet and a height of 8 feet
Answer: 30 sq ft
Step-by-step explanation: The area of a triangle can be calculated using the formula A = 1/2 * b * h, where A is the area, b is the base, and h is the height. In this case, the base of the triangle is 7 1/2 feet and the height is 8 feet, so the area is calculated as follows: A = 1/2 * 7.5 * 8 = 30 square feet. Therefore, the area of the triangle is 30 square feet.
Answer:
[tex]30sq ft[/tex]
Step-by-step explanation:
What does infinity x mean?
The term "infinity" in mathematics refers to something that is bigger than a natural number.
Given that,
We have to find what is infinity means.
We know that,
What is infinity?Something that has no beginning is said to be infinite. It is generally something that has no restrictions. It is a condition in which there are no boundaries in terms of time, space, or any other kind of quantity.
Infinity is denoted by ∞.
If there is a one-to-one relationship between a set of numbers and a suitable subset of itself, that set can be said to be infinite.
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A swimming pool has a volume of 32,700 cubic feet. How many gallons of water does the pool hold?.
HELP PLS FAST I WILL MARK THE BRAINLIEST TO WHO IS FIRST
Kally drives 120 kilometers at a speed of 75 kilometers per hour. For how many hours does he drive?
Group of answer choices
A. 1.2 hours
B. 0.8 hours
C. 1.6 hours
D. 1.3 hours
Answer:
1.6
Step-by-step explanation:
Goold helped!!!
PLS SOLVE for please and thank you:))
pls help this is important
Lea bought some books and a reading light. He spent a total of $54. Each book cost $6 and the reading light costs $12. How many books did he buy?
Select an equation that could be used to answer the question above. Let b represent the number of books.
A. 54+6b+12
B. 54 - 12b = 6
C. 6b+ 12=54
D. 12b-6=54
Given the following two ordered pairs calculate the rate of the function.
(−9, −4) and (−3, −16)
Enter your answer in the box.
m=
Answer:
m=-2
Step-by-step explanation:
Recall slope (m) can be found using the following:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
For this problem, let:
[tex](x_1,y_1)=(-9,-4)\\(x_2,y_2)=(-3,-16)[/tex]
So,
[tex]m=\frac{(-16)-(-4)}{(-3)-(-9)}\\m=\frac{(-16)+4}{(-3)+9}\\m=\frac{-12}{6}\\m=-2[/tex]
Если большой металлический шар данного радиуса R расплавить и из всего материала вылить одинаковые маленькие шарики радиуса r, то сколько их получится?
R=3см;r=0,5см;π≈3.
Answer: 216 small balls
Step-by-step explanation:
The volume of a ball:
[tex]\displaystyle\\V=\frac{4}{3} \pi R^3[/tex]
Let us calculate the volume of a big metallic ball:
[tex]\displaystyle\\V_{big}=\frac{4}{3} (3)(3^3)\\\\ V_{big}=4(27)\\\\V_{big}=108 \ cm^3[/tex]
Now let us calculate the volume of a big small ball:
[tex]\displaystyle\\V_{small}=\frac{4}{3} (3)(0.5^3)\\\\ V_{small}=4(0.125)\\\\V_{small}=0.5 \ cm^3[/tex]
Thus, the number of identical small balls should work:
[tex]\displaystyle\frac{V_{big}}{V_{small}} =\frac{108}{0.5} \\\\\frac{V_{big}}{V_{small}} =216\ units[/tex]
Is AAS and SAA the same?
Yes AAS and SAA are the same Methods for determining whether two triangles are congruent.
The acronym AAS or SAA stands for "Angle, Angle, Side or Side, Angle, Angle" denoting two angles and a side opposite them. AAS os SAA is one of the five methods for determining whether two triangles are congruent. It states that two triangles are congruent if their vertices are in one-to-one correspondence, that is if two angles and the side that is opposite to one of them in one triangle are congruent to the corresponding angles and the side that is not included in the second triangle. The side that is in opposition to either of the angles that are being used is called the non-include side. In layman's terms, two triangles are congruent if the sides of two pairs of corresponding angles are equal in each triangle.
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A number split by 3 in algebraic expression
Answer:
x/3
Step-by-step explanation:
like x divided by 3
For an investment of $26,245, a quarterly statement reports that the account balance is $26,192. The statement also reports that for the same quarter, the rate of return on the investment was - 0.02%. Given the information regarding the investment's quarterly activity, is the reported rate of return reasonable? Use complete sentences to explain your answer.
The reported rate of return is not reasonable i.e. the rate of return on the investment is -0.20% .
What is Return ?
The annual return on an investment, expressed as a percentage of the initial investment.an investment of $200 earns $12 for a year, so the Rate of Return is 12/200 = 0.06 = 6%.
Given, for an investment of $26,245, a quarterly statement reports that the account balance is $26,192 and rate of return for the same quarter was -0.02 %.
Here, we'll calculate the rate of return as follows:
Rate of return = (change in investment/ Initial investment) × 100
= ($26,192 - $26,245)/$26,245 × 100
= -53/26245 × 100
= - 0.20 %
Hence, The correct rate f return will be -0.20 %, not -0.02%.
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a researcher wants to study students to see if age of students has a positive relationship with grade point average. the researcher will get both age and grade point average from the college but not identifying individual students. grade point average appears to follow the normal curve. which test statistic would you use?
As our sample size is large and grade point average follows normal curve, we use parametric test.
What is normal curve?The normal curve is a statistical measurement which refer that the available data presented in a large number close to the mean value.
What is parametric test?The test is used to determine an approximate value of a set of data.
hence, we use parametric test for determining an approximate value.
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What are the 8 types of functions?
The eight types of functions are Linear Functions, Quadratic Functions, Polynomial Functions, Exponential Functions , Logarithmic Functions, Trigonometric Functions, Rational Functions, Piecewise Functions.
1. Linear Functions: Linear functions are equations of the form y = mx + b, where m and b are constants and x is an independent variable. The equation describes a straight line when graphed. The slope of the line is m, and the y-intercept, where the line crosses the y-axis, is b.
2. Quadratic Functions: Quadratic functions are equations of the form y = ax^2 + bx + c, where a, b, and c are constants and x is an independent variable. These equations describe parabolas when graphed. The vertex of the parabola is the point (x, y) where the curve changes direction and is given by (-b / 2a, c - b^2 / 4a).
3. Polynomial Functions: Polynomial functions are equations of the form [tex]y = a_nx^n + ... + a_1x + a_0,[/tex] where a_n, ..., a_1, a_0 are constants and x is an independent variable. These equations can describe many different shapes when graphed.
4. Exponential Functions: Exponential functions are equations of the form [tex]y = a^x[/tex], where a is a constant and x is an independent variable. These equations describe exponential growth or decay when graphed. The rate of growth or decay is determined by the value of a.
5. Logarithmic Functions: Logarithmic functions are equations of the form y = log_a x, where a is a constant and x is an independent variable. These equations describe logarithmic curves when graphed. The base of the logarithm is determined by the value of a.
6. Trigonometric Functions: Trigonometric functions are equations of the form y = f(x), where f is a trigonometric function (e.g. sin, cos, tan, cot) and x is an independent variable. These equations describe sine and cosine curves when graphed.
7. Rational Functions: Rational functions are equations of the form y = (ax + b) / (cx + d), where a, b, c, and d are constants and x is an independent variable. These equations can describe many different shapes when graphed.
8. Piecewise Functions: Piecewise functions are equations of the form y = f(x) if x is in a certain interval, and y = g(x) if x is in another interval. These equations can describe many different shapes when graphed.
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Can tar and QRS be proven congruent by SAS?
Yes,△TSR is Congruent to △QRS ( i.e,△QRS ≅ △TRS) by SAS , because there is all enough information to prove that the triangles are congruent by SAS rule.
What is SAS Congruence rule?The word "congruent" for figures means the same thing in all respects, mainly shape and size. The relationship between two congruent entities is described by congruence. SAS congruence is a term also known as side angle side congruence. According to this rule, two triangles are congruent if two sides of a triangle are equal to two sides of another triangle and the angles formed by those sides of the two triangles are equal. We have two triangles, △TSR and △QRS as we can see in above figure and we get ,
RS = RS ( common side)∠RST = ∠RSQ = 90° SQ = ST ( similar as provide )Thus, two sides and one angle of triangle is similar to corresponding sides and angle of other triangle, so SAS Congruence criteria is applicable here. Therefore, △QRS ≅ △TRS by the SAS Congruence Postulate.
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Complete question :
Can TSR and QRS be proven congruent by SAS ? and the triangles are shown above figre.
Find the simple interest
Principal =4800.00
annual interest rate =3%
time= 3 years
The interest earned is = ?
PLS ANSWER THIS IS DUE TOMMOROW
Which classification best represents a triangle with side lengths 10 in. , 12 in. , and 15 in. ?acute, because 102+122>152acute, because 122+152>102obtuse, because 102+122>152obtuse, because 122+152>102.
Answer:
acute, because 10²+12²>15²
Step-by-step explanation:
You want to classify a triangle with sides 10 in, 12 in, and 15 in.
Form factorThe "form factor" (f) of the triangle can be computed as ...
f = a² +b² -c²
where a, b, c are the side lengths in increasing order. This is positive for an acute triangle, negative for an obtuse triangle, and zero for a right triangle.
Applicationf = 10² +12² -15² = 100 +144 -225 = 19
f > 0
That is to say 10² +12² > 15², so the triangle is acute
__
Additional comment
The largest angle in the triangle is arccos(f/(2ab)). In this triangle, that is ...
arccos(19/(2·10·12)) ≈ 85.46°, an acute angle