6/8 = 0.75
0.75 is written in stardard notation, to write it in scientific notation:
1.- Move the decimal point one place to the right.
2.- Write the new number
3.- Write x 10
4.- Write the number of places you move the decimal point as a negative exponent.
0.75 = 7.5 x 10^-1
1.1.4QueName the segments in the figure below.RSelect all that apply.DASTB. TUC. SRE. QUOGOSDIOTD. RSOF OTH.RSJ. TOL. RSNOTOK RTM. QR
In my opinion the names are just
QT, QS, QR, RT, RS, ST
Loretta has a patio in the shapea trapezoid. The floor of the patio is shown in the sketch below.12 feet5 feetWood PlanksBrick15 feetLoretta wants to put trim around the edge of the floor of the patio that is wood planks that does notshare an edge with the brick part. How many feet of trim will she need?
We can calculate the width of the rectangle patio with pythagorean theorem:
[tex]\begin{gathered} \text{Base of triangle=15-12=3} \\ c^2=a^2+b^2 \\ 5^2=3^2+b^2 \\ b=\sqrt[]{25-9} \\ b=\sqrt[]{16} \\ b=4 \end{gathered}[/tex]Then, she need to put trim on the edge of the floow of the patio that is wood planks and DOES NOT share and edge with the brick part:
[tex]\begin{gathered} T=12+4+12 \\ T=28\text{ feet} \end{gathered}[/tex]Loretta need to put 28 feet of trim.
P= a+b+c. Solve for b
We are given
[tex]P=a+b+c[/tex]We are to solve for b
This simply means we are to make b the subject
Hence we have
[tex]\begin{gathered} P-a-c=b \\ b=P-a-c \end{gathered}[/tex]Therefore, the solution is
[tex]b=P-a-c[/tex]Write the first four terms in the expansion of: (x + y)^8
Given:
[tex](x+y)^8[/tex]We will write the first four terms of the expansion.
the general rule of the expansion is as follows:
[tex](x+y)^n=x^n+n*x^{n-1}*y+...+nCr*x^{n-r}*y^r+...+y^n[/tex]So, the answer will be, the first four terms are:
[tex]x^8+8x^7y+28x^6y^2+56x^5y^3[/tex]X is a normally distributed random variable with mean 52 and standard deviation 7.What is the probability that X is between 45 and 59?Use the 0.68-0.95-0.997 rule and write your answer as a decimal.
We know that
[tex]\begin{gathered} \mu=52 \\ \sigma=7 \end{gathered}[/tex]If X is a normally distributed random variable with mean 52 and standard desviation 7, the probability that X is between 45 and 59 is represented as
[tex]P(45Then, we must write 45 and 59 as the mean 52 plus or minus a multiple k of the standard desviation 7[tex]\begin{gathered} 45=\mu+\sigma k \\ 45=52+7k \\ 7k=45-52 \\ k=-1 \end{gathered}[/tex]So,
[tex]45=\mu-\sigma[/tex]By a similar calculation
[tex]59=\mu+\sigma[/tex]This means
[tex]P(45taking into account that X is normally distributed and using the 0.68-0.95-0.997 rule[tex]P(\mu-\sigmaSo, P (45 < X < 59) = 0.68What is the equation for the nth term of the arithmetic sequence where a1 = 30 and d = –9? an = 30 – 9n an = 30 – 9(n – 1) an = 30 + 9n an = 30 + 9(n – 1)
Given:
[tex]a_1=30\text{ and d=-9}[/tex][tex]a_n=a_1+(n-1)d[/tex][tex]a_n=30_{}+(n-1)(-9)[/tex][tex]a_n=30_{}-9(n-1)[/tex]how do I find how many circles would be in the 5th term
You can notice that in the first term there is one circle, in the second term there are three cricles and in the third term are six circles.
Each of the previous term can be expressed as follow:
first term:
[tex]2^0+0=1[/tex]second term:
[tex]2^1+1=3[/tex]third term:
[tex]2^2+2=6[/tex]In gereral, you can write for the (n + 1)th term:
[tex]2^n+n[/tex]Thus, each term of the series can be expressed as the previoues expression indicates. The fourth term is the result for n=3 and the fifth term is the result for n=4. You replace and you obtain:
fifth term:
[tex]2^4+4=16+4=20[/tex]Hence, the fifth term will have 20 circles.
Point P is the image of P (5,-5) under translation by two units to the left and five units up
The coordinate of P' = (3, 0)
Explanation:Given:
Point P coordinate = (5, -5)
Point P was translated by 2 units left and 5 units up to get P'
To find:
The coordinates of the image which is P'
To get the coordinate of P', we will move the point P by 2 units to the left (subtract 2 units from the x coordinate) and add 5 units to the y coordinate
[tex]\begin{gathered} Translation\text{ rule:} \\ translation\text{ to the left: \lparen x, y\rparen}\rightarrow\text{ \lparen x-a, y\rparen} \\ where\text{ a is the number of units moved left} \\ \\ translation\text{ up: \lparen x, y\rparen}\rightarrow(x,\text{ y + b\rparen} \\ b\text{ is the number of units moved up} \end{gathered}[/tex][tex]\begin{gathered} Applying\text{ the translation:} \\ a\text{ = 2 units and b = 5 units} \\ (5,\text{ -5\rparen }\rightarrow\text{ \lparen5 - 2, -5 +5\rparen} \\ =\text{ \lparen3, 0\rparen} \\ \\ The\text{ coordinate of P' = \lparen3, 0\rparen} \end{gathered}[/tex]4. Solve the equation using square roots.x2 + 10 = 9x^2+10x=9
Given:
The area of the playground is 204 square yd.
The width of the playground is 5 yd longer than its length.
Let, w be the with of the playground and l is length.
[tex]w=5+l[/tex]The area is given as,
[tex]\begin{gathered} A=l\times w \\ 204=l\times(l+5) \\ l^2+5l-204=0 \\ Use\text{ quadratic formula:} \\ l=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a},a=1,b=5,c=-204 \\ l=\frac{-5\pm\sqrt[]{5^2-4\times1\times(-204)}}{2} \\ l=\frac{-5\pm\: 29}{2} \\ l=\frac{-5+29}{2},l=\frac{-5-29}{2} \\ l=12,l=-17 \end{gathered}[/tex]As length can not be negative.
Hence, length = l =12 yd
Width = w = l +5 = 12+5 =17 yd.
Answer: owidth is 17 yds.
The difference of w and 3 is less than 29
The difference of w and 3 is less than 29
so
w-3 < 29the image is downloading now
Problem N 2
A number x increased by 4 is greater than -19
x+4 > -19Problem N 3
The quotient of c and 2 is at least -23
[tex]\frac{c}{2}\ge-23[/tex]7.8.1y varies directly as x. y = 50 when x= 5. Find y when x= 16.y =(Simplify your answer.)
If y varies directly as x
x=5 when y= 50
so we can assumme the next equation
y=10x
so
x=16 y=10(16)=160
Simplify and state restrictions. Show the factors before cancelling. 2x2-6x x2-9 . 4x3+28x2 x2+8x+15
Solution:
Given:
[tex]\frac{2x^2-6x}{x^2-9}\div\frac{4x^3+28x^2}{x^2+8x+15}[/tex][tex]\begin{gathered} \frac{2x^2-6x}{x^2-9}\times\frac{x^2+8x+15}{4x^3+28x^2} \\ \\ To\text{ simplify the expression, we n}eed\text{ to factorize each expression and cancel them out.} \\ \text{Hence,} \\ \frac{2x(x-3)}{(x-3)(x+3)}\times\frac{(x+3)(x+5)}{4x^2(x+7)} \end{gathered}[/tex]Canceling out the common factors,
[tex]\begin{gathered} \frac{2x(x-3)}{(x-3)(x+3)}\times\frac{(x+3)(x+5)}{4x^2(x+7)} \\ \frac{(x+5)}{2x(x+7)} \end{gathered}[/tex]Thus,
[tex]\frac{2x^2-6x}{x^2-9}\div\frac{4x^3+28x^2}{x^2+8x+15}=\frac{(x+5)}{2x(x+7)}[/tex]The restrictions will occur for the expression to be undefined.
The expression will be undefined when the denominator is zero.
[tex]\begin{gathered} \frac{(x+5)}{2x(x+7)} \\ \text{Hence,} \\ 2x(x+7)=0 \\ 2x=0\text{ OR x + 7 = 0} \\ x=\frac{0}{2}\text{ OR x = 0 - 7} \\ x=0\text{ OR x = -7} \\ \\ \text{Hence, there are restrictions at x = 0 and x = -7 because the expression will be undefined at these two points} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \frac{(x+5)}{2x(x+7)}\text{ will have the following restrictions,} \\ x\ne0\text{ and x }\ne-7 \end{gathered}[/tex]-5n = 20Help don’t have time
Simplify the equation.
[tex]\begin{gathered} -5n=20 \\ n=\frac{20}{-5} \\ =-4 \end{gathered}[/tex]So value of n is -4.
Find the volume of the following shape. Round to the tenths place.
To answer this question we will use the following formula to compute the volume of a cone:
[tex]V=\frac{\pi r^2h}{3}.[/tex]Substituting r=9cm and h=10cm in the above equation we get:
[tex]V=\frac{\pi(9cm)^2(10cm)}{3}=\frac{810\pi cm^3}{3}=270\pi cm^3\approx848.2cm^3.[/tex]Answer: 848.2cm³
Ivanna bought some books. She spent a total of $71 after a discount of $5 off of her total purchase. Each book cost $4. How many books did she buy?Write an equation that could be used to answer the question above.
Answer:
19 books
Explanation:
Let the amount of books bought be x
If she spent a total of $71 after a discount of $5, the total amounshe spend on the books will be $76
If each book costs $4,
x books will cost $76
Cross multiply
1 * 76 = x * 4
76 = 4x
Rearrange
4x = 76
Divide both sides by 4
4x/4 = 76/4
x = 19
Hence she bought 19 books
I need some help with these three right here, last tutor I had gave me an explanation but didn't actually help me with the answers
at 1st triangle: all three sides are not similar
second triangle:only two sides are similar
at third triangle all the three sides are similar
Simplify 110011two × 101 two
SOLUTION:
We want to multiply the following binary numbers;
[tex]110011_2\times101_2[/tex]It would be really convenient to convert this to base ten, multiplying and then reconverting to base 2;
[tex]\begin{gathered} 110011_2=51_{10} \\ 101_2=5_{10} \end{gathered}[/tex]Thus, the multiplication gives;
[tex]51\times5=255_{10}[/tex]Converting this back to binary we have the result;
[tex]110011_2\times101_2=11111111_2[/tex]20. In a volleyball game, Caroline served the ball over the net 16 out of 20 times. Whatpercent did she not make her serve over the net?lo
Given:
Number of times Caroline served the ball over the net out of 20 times = 16
Required: Percentage of Caroline did not make her serve over the net
Explanation:
Number of times Caroline not served the ball over the net out of 20 times
[tex]\begin{gathered} =20-16 \\ =4 \end{gathered}[/tex]Percentage of Caroline did not make her serve over the net
[tex]\begin{gathered} =\frac{4}{20}\cdot100\% \\ =20\% \end{gathered}[/tex]Final Answer: Percentage of Caroline did not make her serve over the net is 20%.
9+1=91, 8+2=75, 7+3=61, 6+4=49, 5+5=39, 3+7=?
We can note the following pattern:
[tex]\begin{gathered} 9^2+1+9=81+10=91 \\ 8^2+2+9=64+11=75 \end{gathered}[/tex]and
[tex]7^2+3+9=49+12=61[/tex]Similarly,
[tex]\begin{gathered} 6^2+4+9=36+13=49 \\ 5^2+5+9=25+14=39 \end{gathered}[/tex]So, our pattern matches with the given results.
By applying this pattern to the question, we have
[tex]3+7\Rightarrow3^2+7+9=9+16=25[/tex]Therefore, the answer is: 7+3=25
(9) If an angle is 26° greater than its supplement, find the measure of the angle.
Answer: 103°
Step-by-step explanation:
Let the angle be x
Angle 26° greater than x is x + 26
sum of two supplementary angles is 180°
Now,
x + x + 26 = 180
⇒ 2x + 26 = 180
⇒ 2x = 154
⇒ x = 77
So required angle = 77 + 26 = 103°
If P={1,3,6,7,9} and Q={1,2,4,5,6,7,8), find P n Q.{}{1, 2, 3, 4, 5, 6, 7, 8, 9}{1, 6, 7}{2, 3, 4, 5, 8, 9}
Given:
P={1,3,6,7,9}
Q={1,2,4,5,6,7,8)
We have to find P ∩ Q.
The symbol ∩ insdicates intersection. So, P ∩ Q indicates the intersection of P and Q.
The intersection of two sets P and Q is the set of all elements that are common in both P and Q.
The elements common in both P and Q are 1, 6, 7.
Therefore, P ∩ Q={1, 6,7}.
Rewrite in simplest terms: 5w 9( 6W + 9)
we multiply each term of the parenthesis by -9
[tex]\begin{gathered} 5w+(6w\times-9)+(9\times-9) \\ 5w-54w-81 \end{gathered}[/tex]simplify doing the subtract between terms with w
[tex]\begin{gathered} (5-54)w-81 \\ -49w-81 \end{gathered}[/tex]Solution
[tex]-49w-81[/tex]A translation maps ABC onto A'B'C'. Use the coordinates A(-3, 0), B(4, 2), B'(0, 0), and C'(6, 3) to determine the translation vector and thecoordinates of C.
Given that a translation maps triangle ABC onto A'B'C'.
with coordinates;
[tex]\begin{gathered} A(-3,0) \\ B(4,2) \\ B^{\prime}(0,0) \\ C^{\prime}(6,3) \end{gathered}[/tex]Let us find the translation vector;
[tex]\begin{gathered} B(4,2)\rightarrow B^{\prime}(0,0) \\ \\ <0-4,0-2> \\ <-4,-2> \end{gathered}[/tex]Therefore, the translation vector is;
[tex]<-4,-2>[/tex]Solving for point C;
[tex]\begin{gathered} C(x,y)\rightarrow C^{\prime}(x-4,y-2)=C^{\prime}(6,3) \\ \\ x-4=6 \\ x=6+4 \\ x=10 \\ y-2=3 \\ y=3+2 \\ y=5 \\ C(10,5) \end{gathered}[/tex]Therefore, the coordinate of C is;
[tex]undefined[/tex]lent/Dependent Variables Lesson 22 WHITBY (Block5-6th Grade MATH-Whitby) CTABLO [GRAPTO PROCESS 5 5 [EQUATION (VARIABLES] [VERBAL DESCRIPTION) Independent variable: A baker con produco 40 cookios (0) every hour (h). Dependent variable: What is the DEPENDANT variable in this problem? * (1 Point) O number of hours Activate Wing Go to Settings to total number of cookies a
In the problem, the number of cookies depend upon the number of hours, as increase in number of hours increase number of cookies and decrease in number of hours decrease the number of cookies.
So cookies is dependent variable and number of hours is independent variable.
Thus, dependent variable is number of cookies.
find the derivative of [tex]h(x) = {4}^{ \frac{x}{2} } \sin(2x) [/tex]
The given expression is:
[tex]\begin{gathered} \\ h(x)={4}^{\frac{x}{2}}\sin (2x) \end{gathered}[/tex]To find the derivative, use the product rule:
[tex]\begin{gathered} \frac{dh}{dx}=\text{ U}\frac{dV}{dx}+V\frac{dU}{dx} \\ U=4^{\frac{x}{2}} \\ \frac{dU}{dx}=\text{ }\frac{4^{\frac{x}{2}}\ln 4}{2} \\ V\text{ = sin(2x)} \\ \frac{dV}{dx}=\text{ 2}\cos (2x) \end{gathered}[/tex]Substitute, U, V, dU/dx, and dV/dx into the product rule given above:
[tex]undefined[/tex]Determine if the following side lengths could form a triangle. Prove your answer with an inequality 28,50,22
Remember that
The Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than the measure of the third side
You only need to see that the two smaller sides are greater than the largest side
In this problem
we have
28,50,22
so
28+22 > 50
50 > 50 -----> is not true
therefore
the following side lengths not form a trianglethe life of a AA battery can be predicted by the number of hours of use as a number of hours of use increases of the remaining battery power decreases to the linear Association is demonstrated in the scatterplot below is Tyler used 20% of the battery power in his AA battery for approximately how many hours has he use the battery
By the plotted graph, we can see that he used 20% of the battery, means the battery is 80% charged. Then, by the graph we can say that he has used the battery for 6 hours.
The Shake Shop sells their drinks in cone-shaped cups that are 7 inches tall. The small size has a diameter of 3 inches, and the large size has a diameter of 5 inches Use 3.14 for it
We get that the volume of the small cup is:
[tex]V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h=\frac{1}{3}\cdot3.14\cdot(\frac{3}{2})^2\cdot7\approx16.5in^3[/tex]Simplify: 2/5÷2 3/4
Solution
Solution
[tex]\begin{gathered} \frac{2}{5}\text{ }\div\text{ 2}\frac{3}{4} \\ \\ \frac{2}{5}\text{ }\div\text{ }\frac{11}{4} \\ \\ \frac{2}{5}\text{ }\times\text{ }\frac{4}{11} \\ \\ \frac{8}{55} \end{gathered}[/tex]Final answer
[tex]\frac{8}{55}[/tex]how to solve the area of the box as a product and sum
From the box we know that the area as a product is given by:
[tex]3x(6x^2-x+9)[/tex]And the result as a sum is given by:
[tex]18x^3-3x^2+27x[/tex]Then:
[tex]3x(6x^2-x+9)=18x^3-3x^2+27x[/tex]