A solution to an equation is a value that, when substituted for the variable, makes the equation true. In the equation x+2=7, the solution is x=5.
This is because if we substitute 5 for x, the equation becomes 5+2=7, which is a true statement. To find this solution, we need to solve the equation by subtracting 2 from both sides, leaving us with x=5. This solution works because it satisfies the equation; when we substitute 5 for x, the equation is true.
In equations, solutions are important because they are the values that make the equation true. Without solutions, equations would remain unsolved and incomplete, which is why it is important to find the solution to an equation.
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Sketch the curve with the given vector equation by finding the following points. (Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) r(t) = (t, 9 – t, 2t) r(-9) (x, y, z) r(0) (x, y, z) r(9) (x, y, z)
For sketching the graph we need to know the coordinate of the vector which are r(1) = ⟨−1, 2⟩, r′(1) = ⟨1, 2⟩
Given:-
x = t − 2,
y = t² + 1 ⇒ t = x + 2
⇒ y = (x + 2)2 + 1
⇒ y = x² + 4x + 5
For find r′(t) we have to ,
r′(t) = ⟨1, 2t⟩
To sketch the position vector r(t) and the tangent vector r′(t) for t = 1.
r(1) = ⟨−1, 2⟩, r′(1) = ⟨1, 2⟩
See the above figure. The red vector is r(1) and the blue one is r′(1)
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show that if \lamdba is in the point spectrum, the the conjugate is in the union of the point and residual spectra of the adjoint
We are given that [tex]\overline\lambda[/tex] is in the point spectrum and we are to prove that the conjugate is the union of the point and residual spectra of the adjoint.
If [tex]\overline\lambda[/tex] ∈ σp(T∗), then T∗v = [tex]\overline\lambda[/tex]v for some v ∈ D(T∗).
Hence, for all u ∈ D(T) we have -
⟨Tu,v⟩ = ⟨u,T∗v⟩ = ⟨u,[tex]\overline\lambda[/tex]⟩ = λ⟨u,v⟩,
⟨(T−λ)u,v⟩ = 0, for all u ∈ D(T)
If λ ∈ σp(T∗), then T∗v = [tex]\overline\lambda[/tex]v for some v∈D(T∗).
Hence, for all u∈D(T), we have ⟨Tu,v⟩=⟨u,T∗v⟩=⟨u,[tex]\overline\lambda[/tex]v⟩=λ⟨u,v⟩,
and therefore,
⟨(T−λ)u,v⟩=0, for all u∈D(T)
i.e. the range of T−λ is not dense and we will have λ ∈ σr(T) ∪ σp(T).
Hence, proved.
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Modeling multiplication and division fraction pls help
The area of each section is 3/4 square feet. To solve the give question use division operation.
What is mixed fraction?
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder.
Given that the area of the garden is [tex]5\frac{1}{4}[/tex] square feet.
Now convert the mixed fraction with improper fraction:
[tex]5\frac{1}{4}[/tex] = [(5×4) + 1]/4
[tex]5\frac{1}{4}[/tex] = 21/4
We have to divide the area 7 equal area.
Thus divide 21/4 by 7.
21/4 ÷ 7
To convert the division sign into multiplication sign, take the reciprocal of 7:
21/4 × 1/7
= (21 × 1)/(4 × 7)
Divide the denominator and numerator by 7:
= 3/4
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Enter the missing values below.
83
18xy +48x y
25
(3x+8y²)
According to the given algebraic expression the missing value is [tex]$18 x^8 y^3+48 x^2 y^5= 6x^2y^3 \left(3 x^6+8 y^2\right)$$[/tex].
What is the formula for algebraic expressions?An equation that includes constants, variables, and a few algebraic procedures is said to be algebraic. A good example of an algebraic equation is 3x2 2xy + d. So, three different sorts of fundamental building blocks make up an algebraic expression: Correlation (i.e. integers) (i.e. numbers)
Which five algebraic expressions are there?The subsequent five categories provide further categorization of various algebraic expression forms. These include the monomial, polynomial, binomial, trinomial, and multinomial.
Briefing:[tex]$6.3 x^2x^6 y^3+8.6 x^2 y^3y^2[/tex]
[tex]$18 x^8 y^3+48 x^2 y^5= 6x^2y^3 \left(3 x^6+8 y^2\right)$$[/tex]
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The complete question is-
[tex]\\$factor the algebraic expression.\\$$18 x^8 y^3+48 x^2 y^5=x-y-\left(3 x^6+8 y^2\right)\\\\$Enter the missing values below\\\\$18 x^8 y^3+48 x^2 y^5=\square x\square y\square (3 x^6+8 y^2)$$[/tex]
Figure 1 and 2 are shown in the coordinate below.
Saorise claims the there is a sequence of transformations that Carries figure 1 onto figure 2. Select all actions that she could take to justify this claim
A. show that a rotation of 180° counterclockwise about the origin carries Figure 1 onto Figure 2
B. show that a reflection over the x-axis followed by a reflection over the y-axis carries Figure 1 onto Figure 2
C. show that a translation of 4 units right followed by a translation of 5 units down carries Figure 1 onto Figure 2
D. show that a rotation of 90° clockwise about the origin followed by a reflection over the x-axis carries Figure 1 onto Figure 2
Answer:
A and B
Step-by-step explanation:
actually the 180° rotation does the same as the reflection over the x-axis and then the reflection over the y-axis.
in a homicide case different witnesses picked the same man from a line up. the line up contained 5 men. if the identifications were made by random guesses, find the probability that all witnesses would pick the same person. round to seven decimal places.
Rounding to seven decimal places, the probability that one individual would be selected by all witnesses is 0.0000128.
Six different witnesses chose the same individual from a lineup in a homicide case. There were 5 guys in the lineup. The likelihood that each of the six witnesses would choose the same person if the identifications were done based just on guesswork.
P = 1 ÷ 5 is the likelihood that a witness will choose a certain individual at random.
The likelihood that all seven witnesses would select the same subject is P = [tex](\frac{1}{5})^{7}[/tex]= 0.0000128.
Simply put, the probability is the likelihood that something will occur. We can discuss the probabilities of different outcomes to determine how likely they are if we are unclear about how an event will turn out.
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Using traditional methods, it takes 100 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 260 students and observed that they had a mean of 99 hours. Assume the standard deviation is known to be 6. A level of significance of 0.01 will be used to determine if the technique performs differently than the traditional method. Find the value of the test statistic. Round your answer to 2 decimal places.
The value of the Test statistic =z=-1.67
We have the value of sigma = 6, n = 260
In a hypothesis test, a test statistic—a random variable—is computed from sample data. To decide whether to reject the null hypothesis, you can utilize test statistics. Your results are compared to what would be anticipated under the null hypothesis by the test statistic. The p-value is computed using the test statistic.
Now using the formula of Test static
Test statistic will be: [tex]\mathrm{z}=\frac{\overline{\mathrm{x}}-\mu}{\frac{\sigma}{\sqrt{\mathrm{n}}}}\\[/tex]
Where, n = total number of sample = 100
[tex]\bar x[/tex] = mean of the given data
[tex]\mu[/tex] = total number of hours taken to receive a basic driving licence.
So, putting the value given in the question,
We will get the value of test static as:
[tex]=\frac{99-100}{\frac{6}{\sqrt{260}}}=-1.67[/tex]
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Find all values of x for which f(x)=3x^4+4x^3-120x^2+120 has local maxima and minima, as well as the inflection points. Please show all of your work.
The Local maxima and minima will be at X = 0 , 4 , -5 and point of inflation will be at [tex]\frac{(-1 + \sqrt{61})}{3},[/tex] [tex]\frac{(-1 - \sqrt{61})}{3}[/tex].
What is Maxima and Minima ?The curve of a function has peaks and troughs called maxima and minima. A function may have any number of peaks and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, while minima will be its lowest.
Extrema is the result of maxima and minima combined. The graph in the graphic below shows several peaks and falls. We obtain the function's maximum and lowest values at x = a and 0 respectively, and at x = b and c respectively. The valleys are the minima and all the peaks are the maximum.
The peaks and minima of the function that appear in a certain interval are known as local maxima and minima. The value of a function at a place in a certain interval for which the values of the function near that point are always smaller than the value of the function at that point would be considered a local maximum. Local minima, on the other hand, would be the value of the function at a location where the values of the function nearby are higher than the value of the function at that location.
When the concavity of a function's graph (or picture) changes, a point of inflection is identified. We need to determine where the second derivative of the function switches from negative to positive, or vice versa, in order to determine this in algebra. So, we calculate the provided function's second derivative.
The fuction is :
[tex]3x^{4} + 4x^{3} -120x^{2} + 120[/tex]
So for local Maxima and minima first derivatives should be zero
Therefore,
[tex]\frac{d}{dx}\\[/tex] ([tex]3x^{4} + 4x^{3} -120x^{2} + 120[/tex] ) = 0
⇒ [tex]12x^{3} + 12x^{2} - 240x = 0[/tex]
⇒ [tex]x^{3} + x^{2} - 20x = 0[/tex]
⇒[tex]x(x^{2} + x - 20) = 0 \\[/tex]
⇒x(x-4)(x+5) = 0
For x = 0, 4 , -5 there is a local maxima or minima.
Now for Point of Inflation second derivative is zero
Therefore,
[tex]\frac{d^{2} }{dx^{2} }[/tex] ( [tex]3x^{4} + 4x^{3} -120x^{2} + 120[/tex]) = 0
⇒ [tex]\frac{d}{dx}[/tex][tex]12x^{3} + 12x^{2} - 240x = 0[/tex]
⇒ [tex]36x^{2} + 24x - 240 = 0[/tex]
⇒[tex]3x^{2} + 2x - 20 = 0[/tex]
⇒ x = [tex]\frac{(-1 + \sqrt{61})}{3},[/tex] [tex]\frac{(-1 - \sqrt{61})}{3}[/tex]
So the point of inflations are [tex]\frac{(-1 + \sqrt{61})}{3},[/tex] [tex]\frac{(-1 - \sqrt{61})}{3}[/tex].
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convert the following equation into standard form.
Y= -2x+6
Answer:
x = 3+y
Step-by-step explanation:
is your ans .................
During one flu epidemic the proportion of adults nationwide who have come down with the flu is 8%. The manufacturer of a flu vaccine claims that those who have been vaccinated are less likely to catch the flu.
The hypotheses are as follows:
Null hypothesis: proportion of those vaccinated catching the flu = 8%
Alternative hypothesis: proportion of those vaccinated catching the flu < 8%
Select one:
A.
Rejecting the null hypothesis means there is evidence that the proportion of those vaccinated catching the flu is less than 8%
Failing to reject the null hypothesis means there is insufficient evidence to conclude that the proportion of those vaccinated catching the flu is less than 8%.
B.
Rejecting the null hypothesis means there is evidence that the proportion of those vaccinated catching the flu is not equal to 8%
Failing to reject the null hypothesis means there is insufficient evidence to conclude that the proportion of those vaccinated catching the flu is equal to 8%.
C.
Rejecting the null hypothesis means there is insufficient evidence that the proportion of those vaccinated catching the flu is equal to 8%
Accepting the null hypothesis means there is evidence to conclude that the proportion of those vaccinated catching the flu is equal to 8%.
D.
Rejecting the null hypothesis means there is evidence that the proportion of those vaccinated catching the flu is less than 8%
Accepting the null hypothesis means there is evidence to conclude that the proportion of those vaccinated catching the flu is equal to 8%.
The test hypothesis is
H₀: p=0.08 (null hypothesis) and
Hₐ: p<0.08 (alternative hypothesis )
Given that,
8% of adults in the country contract the flu at any given time during a flu epidemic. The following are the hypotheses:
0% of people who received the vaccine contracted the flu.
8% or less of people who received the vaccine ended up getting the flu.
In order to reject the null hypothesis, there must be proof that 8% of individuals who received the vaccine did not also get the flu.
If the null hypothesis is not rejected, then there is insufficient data to draw the inference that the proportion of people who receive the flu shot is 8%.
The test hypothesis is H₀: p=0.08 (null hypothesis) and Hₐ: p<0.08 (alternative hypothesis )
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No. of coffee sales (undred)
2
18
S
10
15
20
Temperature (°C)
25
30
Describe the relationship between the temperature and the coffee
sales
0
As the temperature decreases, the number of coffee sales
decreases
As the temperature increases, the number of coffee sales
increases
As the temperature increases, the number of coffee sales
decreases
D
There is no trend between the temperature and the number of
coffee sales
LT
The relationship between the temperature and the coffee sales is if the temperature decreases then the number of coffee sales decreases.
So, option a is correct.
What is meant by temperature?The SI unit of temperature according to the International System of Units is Kelvin, indicated by the sign K. The Kelvin scale is widely recognized or used in research and engineering. However, the global standard for measuring temperature is the Celsius or Fahrenheit scale. The unit of measurement known as temperature can be expressed on a number of scales, including the Fahrenheit and Celsius systems. Temperature depicts the direction in which heat energy spontaneously moves, i.e., from a hotter (body with a higher temperature) to a colder (body with a lower temperature) (one at a lower temperature).
The relationship between the temperature and the coffee sales is if the temperature decreases then the number of coffee sales decreases.
Hence, option a is correct.
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Amy is going to spend What she saves from her rent budget on entertainment. How much will she’s have for entertainment each month?
Since Amy's rent is 60 percent of the budget for Rent, Utilities, and Food, she will have $853 to spend on entertainment each month.
How is the rent budget determined?The total budget for rent, utilities, and food for nine months is given as $12,798.
Using the mathematical operation of multiplication, the proportion that belongs to rent alone is $7,678.80, representing 60%.
This rental proportion is divided by 9 to determine the monthly budget for rent, which will then be spent on entertainment.
The total budget for rent, utilities, and food for nine months = $12,798
The percentage of the budget for rent = 60%
The amount for rent for nine months = $7,678.80 ($12,798 x 60%)
The monthly rent amount is $853.20 ($7,678.80/9)
Thus, we can conclude that Amy will spend $853 monthly on entertainment if she saves the rent budget.
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Question Completion:The percentage of the rent to the total rent, utilities, and food budget is 60%.
Given f(x)=3x+4 find f(4)
Answer:
Step-by-step explanation:
To find f(4), you can substitute 4 for x in the equation f(x) = 3x + 4. This gives you:
f(4) = 3(4) + 4
= 12 + 4
= 16
Therefore, f(4) = 16.
write x^2+10x+12 in the form (x+a)^2-b
Answer:
(x+5)^2 - 13
Step-by-step explanation:
If you work out the target expression, you get:
(x+a)^2-b = (x+a)(x+a)-b = x^2 + 2ax + a^2 - b
so 2ax must be 10x, hence a = 5
also a^2 - b must be 12, and with a being 5, this means b = 25-12 = 13
Answer:
[tex](x+5)^2 - 13[/tex]
Step-by-step explanation:
In order to convert the given quadratic [tex]x^2 + 10x + 12[/tex] into the form [tex](x+a)^2 - b[/tex], you need to put the given quadratic into vertex form.
⭐What is vertex form?
a way you can rewrite a quadratic equation[tex](x-h)^2 + k[/tex]-(-h) = x-value of the vertex+k = y-value of the vertex⭐How do you rewrite a quadratic in vertex form?
you partially complete the squareI will demonstrate how to "partially complete the square" with the given quadratic.
Given: [tex]x^2 + 10x + 12 = 0[/tex]
Subtract the constant from the LHS and RHS.
[tex]x^2 + 10x = -12[/tex]
Divide the coefficient of the middle term by 2, square that result, and add it to the LHS and RHS.
[tex](\frac{10}{2})^2\\(5)^2\\= 25[/tex]
[tex]x^2 + 10x + 25 = -12 + 25[/tex]
[tex]x^2 + 10x + 25 = 13[/tex]
Write the LHS into the polynomial identity: [tex](a+b)^2[/tex] by factorising
[tex]x^2 + 5x + 5x + 25 = 13[/tex]
[tex]x(x + 5) + 5(x + 5) = 13[/tex]
[tex](x+5)(x+5) = 13[/tex]
[tex](x+5)^2 = 13[/tex]
Subtract 13 from the LHS and RHS.
[tex](x+5)^2 - 13[/tex]
That's it!
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Use spherical coordinates to Find the average distance from a point in a ball of radius a to its center.
The average distance from a point in the ball to its center = [tex]\frac{3}{4}[/tex] A
Given the radius in the question = a
The integration of the total distance before dividing the volume will be =
⇒ [tex]\int_0^{2\pi}\int_0^\pi\int_0^A a\cdot a^2\sin\theta\,da\,d\theta\,d\phi[/tex]
⇒ [tex]\int_0^{2\pi}\int_0^\pi\int_0^A a^3\sin\theta\,da\,d\theta\,d\phi[/tex]
⇒ [tex]\frac{A^{4} }{2}[/tex] [tex]\int_0^{2\pi}\int_0^\pi \sin\theta\,d\theta\,d\phi[/tex]
⇒ [tex]\frac{A^{4} }{2}[/tex] [tex]\int_0^{2\pi}1\,d\phi[/tex]
⇒ [tex]\pi A^{4}[/tex]
Let us divide the average distance by the ball's volume,
⇒ [tex]\frac{\pi a^4}{(4/3)\pi a^3}[/tex]
⇒ [tex]{\frac{3a}4}[/tex]
By the use of the Parcly Taxel's way,
Let the radius of the ball be = A
f(x) = probability density function
Distance = D from the given point to the center.
P( D < a )
[tex]\begin{align}P(D\leq r)&= \frac{ \frac 43 \pi r^3 }{\frac 43 \pi R^3}=\frac {r^3}{R^3}, \ \ \ 0\leq r\leq R. \end{align}[/tex][tex]\frac{\frac{4}{3} \pi a^{3} }{\frac{4}{3} \pi A^{3} } = \frac{a^{3} }{R^{3} }[/tex]. 0 [tex]\leq[/tex] a [tex]\leq[/tex] A
Therefore, The average distance from a point in the ball to its center = [tex]\frac{3}{4}[/tex] A
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Calculate the average rate of change between x=-1 and x=1.
Between x=-1 and x=1, the average rate of change is 1.
What is meant by average rate of change?It represents the average change in the function's per-unit value during that time period. Calculating the average rate of change is very helpful for tracking changes in measurable parameters like average speed or average velocity. As the slope of the straight line that links the two spots, the average rate of change between the two points is determined. Use the formula:
(f(b)-f(a))/(b-a) to get the average rate of change of f(x) between x=a and x=b.
Given line in the figure passes through the points A(4, 0), B(-1, -5)
Let the equation of the line be:
y=mx+ c
Slope m=(-5-0)/(-1-4)
m=1
Therefore, y=x+ c
It passes through (4, 0)
y+ c=0
c=-4
y=x-4=f(x)
f(-1)= -1-4=-5
f(1)= 1-4=-3
The average rate of change=(f(b)-f(a))/(b-a)
=(f(1)-f(-1))/1-(-1)
= -3-(-5)/(1+1)
=2/2
=1
Therefore, Between x=-1 and x=1, the average rate of change is 1.
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Help me with this math please. Help me quick please.
Answer:
f(x) = 5/2x
Step-by-step explanation:
The parent function for the given equation is f(x) = 1/2x. When this function is vertically stretched by a factor of 5, the resulting function will be f(x) = 5/2x. This means that for any value of x, the output of the transformed function will be 5 times greater than the output of the parent function.
For example, if x = 2, then f(x) = 1/2 * 2 = 1 for the parent function, and f(x) = 5/2 * 2 = 5 for the transformed function. Similarly, if x = 3, then f(x) = 1/2 * 3 = 1.5 for the parent function, and f(x) = 5/2 * 3 = 7.5 for the transformed function.
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the quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant, is .
The quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant b^2 - 4ac is either positive or zero .
Given :
the quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant, is .
Quadratic equation :
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0.
Formula :
= -b ± [tex]\sqrt{b^2 - 4ac / 2a}[/tex]
Discriminant = b^2 - 4ac
if b^2 - 4ac = 0 or positive value then only the formula give us the coordinates of the points of intersection of a line .
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The balance on Howard Gessner’s American Express card on August 1 is $543.27. In August, he charges an additional $201.25 of purchases, has returns of $89.22, and makes a payment of $300. If the finance charges are calculated at 1.5% per month on the unpaid balance, find the balance on September 1.
Mathematically, the balance on Howard Gessner's American Express card on September 1 is $360.63.
How do we determine the balance?The ending balance on September 1 is determined using the mathematical operations of addition, subtraction, and multiplication (for the finance charge).
The finance charge is the interest and other fees paid for borrowing credit.
The finance charge is always based on a percentage, called the annual or monthly percentage rate (APR or MPR).
In this situation, the monthly percentage rate is applied to the unpaid balance (multiplication) at the end of August, to determine the finance charge, which is added to the unpaid balance to compute the September 1 balance.
August 1 Balance = $543.27
Purchases 201.25
Returns (89.22)
Payments (300.00)
Unpaid balance $355.30
Finance charge 5.33 ($355.30 x 1.5%)
September 1 Balance $360.63
Thus, using mathematical operations, the balance on September 1 is $360.63.
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State the degree and leading coefficient of the polynomial in one variable. If it is not a polynomial in one variable, explain why.
n+8
degree =
leading coefficient =
Answer: The degree of a polynomial is the highest exponent of the variable in the polynomial. The leading coefficient of a polynomial is the coefficient of the term with the highest degree.
In the expression "n + 8", the highest degree of the variable is 1 and the coefficient of the term with the highest degree is 1. Therefore, the degree of the polynomial is 1 and the leading coefficient is 1.
So, the degree of the polynomial is 1 and the leading coefficient is 1.
Note: If the expression had included terms with higher degrees of the variable, such as "n^2 + 3n + 8", the degree of the polynomial would have been 2 and the leading coefficient would have been 1.
I need help with my math homework
The multiplications, applying the associative property, are given as follows:
1. (5 x 2) x 3 = 10 x 3 = 30.
2. 4 x (3 x 3) = 4 x 9 = 36.
3. (6 x 1) x 4 = 6 x 4 = 24.
4. 5 x (2 x 4) = 5 x 8 = 40.
5. (2 x 2) x 8 = 4 x 8 = 32.
6. 3 x (2 x 2) = 3 x 4 = 12.
7. (4 x 2) x 4 = 8 x 4 = 32.
8. 6 x (3 x 3) = 6 x 9 = 54.
What is the associative property of multiplication?The associative property of multiplication defines that the order in which the factors are multuiplied does not change the product.
In this problem, we have to consider that the parenthesis gives the precedence of the factors, meaning that the terms inside the parenthesis are multiplied first, and their result should be placed on the blanks below the parenthesis.
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if a crew of six workers completes a job in 15 hours how long will it take 10 workers to complete the same job
As no. of crews and time are inversely proportional 10 workers will finish the job in 10 hours.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, A crew of six workers completes a job in 15 hours.
We know more crew will finish the job in less no. of hours so they are inversely proportional.
So, C = k/t.
6 = k/15.
k = 90.
Now, C = 10 hence,
10 = 90/t.
t = 90/10.
t = 10 hours.
So, They can finish in 10 hours.
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8. The number 86.345 correct to one decimal place is
Answer:
86.3
Step-by-step explanation:
86.345
step 1
identify their place values
8 — Tens
6 — Units
.3 — tenth( 1 decimal place)
.34 — Hundredth (2 decimal place)
.345 — Thousandth ( 3 decimal place)
to one decimal place is
= 86.3
remember 4 is a round down number so .345 can't actually affect the 3
i hope this answered helped.
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Solve for X : x + (7 x5) = 25
Franco said 9.37×0.1=93.7 is he correct
Answer:
No, Franco's calculation is incorrect.
Step-by-step explanation:
No, Franco's calculation is incorrect. The correct answer is 9.37 x 0.1 = 0.937.
When multiplying a decimal number by a decimal number, the decimal point in the product should be placed so that the number of decimal places in the product is equal to the sum of the number of decimal places in the factors. In this case, the number 9.37 has two decimal places, and the number 0.1 has one decimal place. Therefore, the product of 9.37 x 0.1 should have a total of 2 + 1 = 3 decimal places.
To obtain the correct answer, we need to multiply 9.37 x 0.1 using standard long multiplication:
Copy code
9.37
x 0.1
0.937
Therefore, the correct answer is 0.937, not 93.7 as Franco stated.
Answer:
No. This is incorrect.
Step-by-step explanation:
9.37 × 1 = 9.37
Times by 1 the number stays the same.
If you multiply by 0.1 the decimal will move one place and the 9.37 should get smaller! The sentence in the problem shows 93.7 which is bigger.
9.37 × 10 = 93.7
9.37 × 0.1 = 0.937
19 points all i have really..Gavin is hoping to buy his first car in 3 years. He is considering two options to help him save and grow his money. If he currently has $800, should he deposit his money into a savings account that is compounded annually at an interest rate of 9% or in a savings account that is compounded quarterly at an interest rate of 3%?
Gavin should deposit his money into a savings account that is compounded annually at an interest rate of 9%.
What is compound interest?
The interest earned on savings that is computed using both the original principal and the interest accrued over time is known as compound interest.
Given that the current balance is $800.
There were two types of schemes.
First scheme offer compounded annually at an interest rate of 9%
Second scheme offer compounded quarterly at an interest rate of 9%.
The formula of compound interest annually is
A = P(1+r)^t
P = principal = 800
r = rate of interest = 9% = 0.09
t = time = 3 year
A = 800(1+0.09)³
A = 1036.02.
The formula of compound interest annually is
A = P(1+(r/n))^tn
P = principal = 800
r = rate of interest = 3% = 0.03
t = time = 3 year
n = 4
nt = 4×3 =12
A = 800(1+0.03/4)¹²
A = 875.04
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A subscription to a program normally costs $36 but is on sale for 25% off. A 7% tax is added at checkout. What is the total cost? $28.89 $45.59 $9.00 $27.00
Answer:
$28.89
Step-by-step explanation:
he subscription is on sale for 25% off, so the cost is $36 - (25% * $36) = $36 - $9 = $27.
Then, a 7% tax is added at checkout, so the total cost is $27 + (7% * $27) = $27 + $1.89 = $28.89.
Therefore, the total cost is $28.89.
Answer:
Step-by-step explanation:
36 will be 27 and 7% of 27 should be added 1,89 so 28,89
The restaurant has 25 boxes of ketchup.
Each box has 250 packets of ketchup.
How many packets of ketchup does the restaurant have?
Answer: 6,250
Step-by-step explanation: As the equation states there are 25 boxes with 250 packs of ketchup take the 25 boxes and multiply the 250 packets
250x25=6,250
please help its holding back my grade 50 points
Answer:
X=54
Step-by-step explanation:
equate both the equations since angles of opposite sides are equal
2x+2=3x-52
3x-2x= 52+2
x=54
answer:
x=54
Step-by-step explanation:
2x+2=3x-52
move the 2x to 3x because x can't be negative
and add 52 to 2 so x=54
the value of y varies directly with x.when y=75 x=1/2 what is the value of y when x equals 2 1/4
The value of y from the equation y = 150x when x = 2(1/4) is 337.5.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 - 9 is an equation.
We have,
y varies directly with x.
y ∝ x
y = kx
Now,
y = 75 when x = 1/2
75 = k(1/2)
k = 75 x 2
k = 150
Now,
y = kx
y = 150x
When x = 2(1/4) = 9/4
y = 150 x 9/4
y = 337.5
Thus,
The value of y is 337.5.
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