Answer:
[tex]5.8\text{ }\times\text{ 10}^2[/tex]Explanation:
Here, we want to write the given number in standard notation
The form we have given, is the scientific notation
To write in the standard form, we consider the scientific notation as they are the same
We have the standard notation as:
[tex]5.8\text{ }\times\text{ 10}^2\text{ = 5.8 }\times\text{ 10}^2[/tex]A Scientist uses 10 grams of carbon evrey 15 mins during an experiment. If the experiment lasted 3 hours, how many total kilograms of carbon did they use
We know that
• A scientist uses 10 grams every 15 minutes.
To find the kilograms used in 3 hours, first, we transform 10 grams into kilograms
[tex]\frac{10}{1000}kg=0.01\operatorname{kg}[/tex]Then, we use the following proportion
[tex]\frac{0.01\operatorname{kg}}{x}=\frac{15\min }{180\min }[/tex]Because 3 hours is equivalent to 180 minutes. Let's solve for x
[tex]\begin{gathered} x=\frac{180\cdot0.01}{15} \\ x=0.12 \end{gathered}[/tex]Hence, the total kilograms are 0.12.20 points 2. Krisstopher was driving to Houston from Pasadena, he drives a 2 3/4 miles and stops for a break. He then drives 5 1/2 miles to reach his destination. What distance in miles did Krisstopher travel to reach his final destination. 81/4 miles 71/2 miles 81/2 miles 6 1/3 miles Clear selection
Add 2 + 3/4 + 5 + 1/2
this gives (2+5) + ( 3/4+2/4)
7 + 5/4 = 8.25
In a video game, Connor scored 25% more points than Max. If c is the number of points that Connor scored and m is the number of points that Max scored. Write an equation that represents the situation.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Connor scored = c
Max scored = m
equation = ?
Step 02:
Connor scored =>>> + 25% Max scored
c = m + m * 0.25
c = m ( 1 + 0.25)
c = 1.25 m
The answer is:
c = 1.25 m
Joy has $68,020 in a savings account that earns 13% annually. The interest is not compounded. How much will she have in 5 years?
A = P + I
A is the new value
P is the initial value
I is the interest
I = PRT
R is the rate in decimal
T is the time
Joy has $68020
P = 68020
The account earns 13% annually
R = 13% = 13/100 = 0.13
The time is 5 years
T = 5
Let us find I, then A
I = 68020(0.13)(5)
I = 44213
Now let us find A
A = 68020 + 44213
A = $112233
She has $112233 in 5 years
Find the product 54,612 x 46?
Explanation
Step 1
Multiply. as you would with whole numbers.( ignore the comma)
so
[tex]\begin{gathered} 54,612x46\rightarrow54612\cdot46=2512152 \\ \end{gathered}[/tex]Step 2
Count the total number of decimal places in your factors.
[tex]54,612\rightarrow\text{3 numbers in decimal places}[/tex]Step 3
Move the decimal point in the product one place to the left for each decimal place you counted.
so
[tex]2512152\rightarrow3\text{ places}\rightarrow2512,152[/tex]so, the answer is
[tex]2512,152[/tex]I hope this helps you
find the percent notation for 0.376
To convert a decimal into a percentage we have to multiply the decimal by 100, as follows:
[tex]0.376\cdot100=37.6\text{ \%}[/tex]0.376 is equivalent to 37.6 %
Question 3(Multiple Choice Worth 3 points)
(01.02 MC)
Joaquin wants to make his famous chocolate chip cookies to bring to his friend's birthday party. The original recipe serves 5 people and requires 1/4 a cup of butter but he needs to serve 28 people. How many cups of butter will he need?
Answer:
B
Step-by-step explanation:
A triangle has vertices on a coordinate grid at D(-5, -2), E(-5,4), andF(-1,4). What is the length, in units, of DE?
To find the length of DE,
Here D = (-5,-2) and E = (-5,4).
Hence the distance is given by
[tex]DE=\sqrt[]{(-5+5)^2+(4+2)^2}[/tex]On simplifying,
[tex]\begin{gathered} DE=\sqrt[]{6^2} \\ DE=6 \end{gathered}[/tex]Hence the length of DE is 6 units
- Which subsets of the real number system does -2.8 belong? A.Rational and Integer.B.Irrational and Integer.C.Irrational onlyD. Rational only.
Answer:
D. Rational only.
Step-by-step explanation:
-2.8 is only rational.
It is not irrational because it is rational(decimal numbers are rational).
It is not integer because there is a decimal part.
So, the correct answer is:
D. Rational only.
Can anyone help me with this a 7 more problem
We are given the following statement.
If a number is an integer, then it is either positve or negative.
In the above statement, the 1st part is the condition and the 2nd part is conclusion.
Condition = a number is an integer
Conclusion = it is either positve or negative
Therefore, the conclusion of the conditional is option B.
A number is either positive or negative.
Dan paid three times as much as Greg for his dinner. (Translate the given situation into an equation. Pick the variable you use according to the context.
Let d represent Dan payment and let g represent Greg payment
"Dan paid three times as much as Greg for his dinner" can be represented as
d= 3g
Number 2
Let x represent the cost of Gym A and Y represent the cost of Gym B
Since Gym B cost twice as much as Gym A
Then y=2x
Number 3
Let d represent Diana's race and let c represent Calorine's race
Diana = 3 x Calorine
d=3c
A fashion designer makes and sells hats. The material for each had cost three dollars. The hats sell for $13.50 each. The designer spends $2121 on fixed cost: advertising, Power, water, rent . How many hats mustard designers sell to break even
The designer spends $2121 and $3 each for hat and he can sell it for $13.50 each.
If there are x number of hats, it will cost him (2121 + 3x) and he can gain 13.50x
The break even is when the cost and sales are equal.
Equating both expressions :
[tex]\begin{gathered} 2121+3x=13.50x \\ 2121=13.50x-3x \\ 2121=10.50x \\ x=\frac{2121}{10.50}=202 \end{gathered}[/tex]The answer is 202 hats
which choices are equivalent to the expression below? check all that apply.[tex] 4\sqrt{6} [/tex]a. [tex] \sqrt{96} [/tex]b.[tex] \sqrt{24} [/tex]c. 96d. [tex] \sqrt{4} \times \sqrt{36} [/tex]e.[tex] \sqrt{16} \times \sqrt{6} [/tex]f.[tex] \sqrt{32} \times \sqrt{3} [/tex]
To find the equivalents of this expression we can write it another way:
[tex]4\cdot\sqrt[]{6}=\sqrt[]{16\cdot6}=\sqrt[]{4\cdot4\cdot6}=\sqrt[]{2\cdot2\cdot2\cdot2\cdot2\cdot3}[/tex]We can group the 2's and 3 however we want and the expression will be the same.
If we do the multiplication of all of them (or 16 times 6, is the same) we get that it's 96, so option a is one equivalent
[tex]\sqrt[]{96}[/tex]Then from the second term we have that another equivalent is
[tex]\sqrt[]{16}\cdot\sqrt[]{6}[/tex]Because the square root can be distributed into the product. So option e is equivalent
If we multiply all the 2's we get that it's 32, so another equivalent is:
[tex]\sqrt[]{32}\cdot\sqrt[]{3}[/tex]Option f is equivalent
Suppose a sample of 383 Americans over 21 is drawn. Of these people, 280 don't smoke. Using the data, construct the 80% confidence interval for the population proportion of Americans over 21 who smoke. Round your answers to three decimal places.
The 80% confidence interval for the population proportion of Americans over 21 who smoke is: 0.240; 0.298.
How to find the confidence interval?First step is to find the population proportion p
Sample size = n = 383
Using this formula to find the population proportion (p)
p = x /n
Let plug in the formula
p = (383 - 280) / 383
p = 103/383
p = 0.2689
Second step is to find the Margin of error (MOE)
Value of z-score for a confidence level of 80%= 1.282
Using this formula to margin of error
MOE =( z alpha x √(p) (1-p) / n )
Let plug in the formula
MOE =( 1.282x √(0.2689)(1-.0.2689) / 383)
MOE =( 1.282 x √(0.2689)(0.7311) / 383)
MOE =( 1.282 x √0.000513297
MOE =( 1.282 x 0.0226561)
MOE = 0.02905
Third step is to find the confidence interval (CI)
Confidence interval = p ± MOE
Confidence interval = 0.2689 ± 0.02905
Confidence interval = ( 0.2689 - 0.02905) , (0.57 + 0.02905)
Confidence interval = 0.23985; 0.29795
Confidence interval = 0.240; 0.298 ( Three decimal places)
Therefore the CI is 0.240; 0.298.
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Solve 9abs(3n-2) + 6 > 51 and graph on the number line
Solving the inequality,
[tex]\begin{gathered} 9\lvert3n-2\rvert+6>51 \\ \rightarrow9\lvert3n-2\rvert>45 \\ \rightarrow\lvert3n-2\rvert>5 \end{gathered}[/tex]Remember that if
[tex]\lvert u\rvert>a,a>0\Rightarrow u<-a\text{ or }u>a[/tex]This way, we get:
[tex]\begin{gathered} 3n-2<-5\rightarrow3n<-3\rightarrow n<-1 \\ 3n-2>5\rightarrow3n>7\rightarrow n>\frac{7}{3} \end{gathered}[/tex]As an interval, we get:
[tex]\: \mleft(-\infty\: ,\: -1\mright)\cup\mleft(\frac{7}{3},\: \infty\: \mright)[/tex]In the number line, we get:
You have a bag of 36 ounces of popcorn. Your friend eats 1/4 of the bag. You eat 1/3 of the bag. How many ounces did you eat? How many ounces are left?
Answer: You Eat: 12 ounces. There are 15 ounces left.
Step-by-step explanation:
36(1/4)=9 ounces
36(1/3)=12 ounces, which is how much you eat.
36-12-9=15 ounces left
Step-by-step explanation:
How many ounces did you eat?
¼+⅓=3+4/12=7/12 ounces were eaten
How many ounces are left?
36-7/12=432-7/12
=425/12
=\frac{425}{12}
=35^5/12
Find the value of 4² + 6².
Answer:
Step-by-step explanation:
52
Answer: The correct answer is 52
Step-by-step explanation:
4² + 6²
4*4 + 6*6
16 + 36 = 52
2) Find the volume of a shoe box that is wide9, 15 inches, and 6 inches high.
volume of the shoe box is 1080 inches³
Explanation:2) The shoe box is rectangular prism
So we will find the volume of a rectangular prism:
Volume of rectangular prism = length × width × height
length = 15 inches
width = 9 inches
height = 6 inches
Volume = 15 × 9 ×6
Volume = 1080 inches³
Hence, the volume of the shoe box is 1080 inches³
The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 34minutes of calls is $25.92, and the remaining credit after 53 minutes of calls is $23.64. What is the remaining credit after 71 minutes of calls?
The remaining credit after 71 minutes is $21.48
To solve this, we can calculate the equation of the linear function that represents the remaining credit
x is the time in minutes, y is the remaining credit. the we have two points of the line and we can calculate the equation
34 min and $25.92 => (34,25.92)
53 min and 23.64 => (53,23.64)
the formula to calculate the slope of a line is
[tex]m=\frac{y_2-y_1}{x_2-x_1_{}}=\frac{23.64-25.92}{53-34}=-0.12[/tex]now we know the slope, we can get the line euqation
[tex]y=m(x-x_1)+y_1\Rightarrow\text{ y=-0.12(x-34)+25.92=-0.12x+30}[/tex]Now for wathever x we ask, just plug it in to the equation and will give you the reamining credit.
for x=71 min:
[tex]y=-0.12(71)+30=-8.52+30=21.48[/tex]theremaining credit is $21.48.
Identify a benchmark you can use to find an equivalent percent for eachratio. Then find the equivalent percent. (Example 1)13. Lo Benchmark: 4. Benchmark:6105.Benchmark:
The benchmark of a fraction a/b is 1/b. Then, for the given:
To find the equivalent percent: find the a/b of 100 :
6/10:
[tex]\frac{6}{10}\cdot100=60[/tex]6/10 =60%___________________
2/4:
[tex]\frac{2}{4}\cdot100=50[/tex]2/4=50%___________________
4/5:
[tex]\frac{4}{5}\cdot100=80[/tex]4/5 = 80%Find the circumference of the circle. Round to the nearest hundredth if necessary. (Use 3.14 for a) A circle with a diameter of 18 in
Given data:
The given diameter of the circle is D=18 in.
The expression for the circumference is,
[tex]C=\pi D[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} C=\pi(18\text{ in)} \\ =56.52\text{ in} \end{gathered}[/tex]Thus, the circumference of the circle is 56.52 in.
I need help number 7
The population at the beginning of 1950 was 2600 thousand people.
Then it started increasing exponentially 23% every decade.
The general form of any exponential function is:
[tex]f(x)=a(b)^x[/tex]Where
a is the initial value
b is the growth/decay factor
x is the number of time periods
y is the final value after x time periods
a. To calculate the growth factor of an exponential function, you have to add the increase rate (expressed as a decimal value) to 1:
[tex]\begin{gathered} b=1+r \\ b=1+\frac{23}{100} \\ b=1.23 \end{gathered}[/tex]b. Considering the initial value a= 2600 thousand people and the growth factor b=1.23, you can express the exponential function in terms of the number of decades, d, as follows:
[tex]f(d)=2600(1.23)^d[/tex]c. Considering that the time unit is measured in decades, i.e d=1 represents 10 years
To determine the corresponding value of the variable d for 1 year, you have to divide 1 by 10
[tex]1\text{year/10years d}=\frac{1}{10}=0.1[/tex]Calculate the growth factor powered by 0.1:
[tex]\begin{gathered} b_{1year}=(1.23)^{0.1} \\ b_{1year}=1.0209\approx1.02 \end{gathered}[/tex]d. Use the factor calculated in item c
[tex]g(t)=2600(1.0209)^t[/tex]Which value is in the solution for the inequality 7 + 3x < 37?
the solution of the inequality will be x<10, i mean all the real numbers that are less than 10. It's because:
[tex]7+3x<37\Rightarrow3x<37-7=30\Rightarrow x<\frac{30}{3}=10[/tex]PLEASE HELP!!!! Explain in depth!!! In a geometry course, the grade is based on the average score on six tests, each worth 100 points. W. Orrier has an average of 88.5 on his first four tests. What is the lowest average he could obtain on his next two tests and still receive an A (an average of 90 or better)?
Answer:
93 marks
Step-by-step explanation:
If he has an average of 88.5 marks on the first four tests then the total score for these four tests is:
[tex]\implies 88.5 \times 4=354[/tex]
To obtain an average of at least 90 marks on each test the total number of marks needed for the six tests is:
[tex]\implies 90 \times 6=540[/tex]
So the minimum total marks he needs to obtain an A is 540.
To find the lowest average he could obtain on his next two tests to still receive an A, subtract the total for the first four tests from the total needed for the six tests and divide by two:
[tex]\implies \dfrac{540-354}{2}=\dfrac{186}{2}=93[/tex]
Therefore, he needs to score an average of at least 93 marks on his next two tests to still receive an A grade.
write an equivalent ratio in simplest form of the ratio 1852 to 3690
926/1845
Explanation:To get the equivalent ratio in its simplest form, wefind the numbers common to both numbers.
[tex]\begin{gathered} \frac{1852}{3690} \\ \end{gathered}[/tex]2 is common to both, so we divide:
[tex]\begin{gathered} 1852\div\text{ 2 = 926 } \\ 3690\div2\text{ = 1845} \\ \frac{926}{1845} \end{gathered}[/tex]We check again if there is a number common to them
No number is common to both numerator and denominator asides 1
Hence, the simplest form is 926/1845
Complete the following statements.
In general, ________% of the values in a data set lie at or below the median.
________% of the values in a data set lie at or below the third quartile (Q3).
If a sample consists of 2100 test scores, ________ of them would be at or below the second quartile (Q2).
If a sample consists of 2100 test scores, ________ of them would be at or above the first quartile (Q1).
In general, 50% of the values in a data set lie at or below the median.
75% of the values in a data set lie at or below the third quartile (Q3).
If a sample consists of 2100 test scores, 1100 of them would be at or below the second quartile (Q2).
If a sample consists of 2100 test scores, 525 of them would be at or above the first quartile (Q1).
What are quartiles?Three values called quartiles divide sorted data into four equal portions with the same amount of observations in each.
One kind of quantile is a quantile. Q1, or the lower quartile, is another name for the first quartile.
Second quartile: Also referred to as the median or Q2.
Third quartile, or the upper quartile, is also referred to as Q3.
The second quartile is 50%
Samples of 2100 test scores that are at or below at the second quartile
= 50% of 2100
= 0.5 * 2100
= 1100
The first quartile is 25%
= 0.25 * 2100
= 525
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An arch is in the shape of a parabola. It has a span of 96 feet and a maximum height of 8 feet.Find the equation of the parabola. ______________Determine the distance from the center at which the height is 2 feet. ___________
We know the equation of a parabola can be written as
y = a(x-b1) (x-b2) where a is a constant and b1 and b2 are the zeros
y = a ( x - 48) ( x - -48)
y = a ( x-48) (x+48)
Now when x = 0 y = 8
8 = a ( 0-48) ( 0+48)
8 = a (-2304)
-8/2304 = a
-1/288 = a
y = -1/288 ( x-48) (x+48)
This is the equation for the parabola
Now let y = 2
2 = -1/288 ( x-48) (x+48)
Multiply each side by -288
-576 = (x-48)(x+48)
FOIL
-576 = x^2- 2304
ADD 2304 to each side
1728=x^2
Take the square root of each side
24 sqrt(3) = x
24 sqrt(3) ft
41.569 ft
Erian's extended family is staying at the lake house this weekend for a family reunion. She is in charge of making homemadepancakes for the entire group. The pancake mix requires 2 cups of flour for every 10 pancakes.[a] Write a ratio to show the relationship between the number of cups of flour and the number of pancakes made.[b] Determine the value of the ratio.c Use the value of the ratio to fill in the following two multiplicative comparison statements..The number of pancakes made is.times the amount of cups of flour needed.The amount of cups of flour needed isof the number of pancakes made.(d If Erian has to make 70 pancakes, how many cups of flour will she have to use?
(a) The ratio is:
[tex]\frac{\text{ number of cups of flour}}{\text{ number of pancakes}}[/tex](b) This ratio is equal to:
[tex]\begin{gathered} \frac{\text{ number of cups of flour}}{\text{ number of pancakes}}=\frac{2}{10} \\ S\text{implifying} \\ \frac{\text{ number of cups of flour}}{\text{ number of pancakes}}=\frac{1}{5} \end{gathered}[/tex](c) Isolating "number of cups of flour":
[tex]\text{ number of cups of flour}=\frac{1}{5}\cdot\text{number of pancakes}[/tex]Isolating "number of pancakes":
[tex]5\cdot\text{ number of cups of flour}=\text{ number of pancakes}[/tex]The number of pancakes made is 5 times the amount of cups of flour needed.
The amount of cups of flour needed is 1/5 of the number of pancakes made.
(d) Substituting with "number of pancakes" = 70, we get:
[tex]\begin{gathered} \text{ number of cups of flour}=\frac{1}{5}\cdot\text{7}0 \\ \text{ number of cups of flour}=14 \end{gathered}[/tex]She will have to use 14 cups of flour
on square PQRS below, if Q is located at (7, 0) and R is located at (5, -8), what is the length of SRleave it in radical form
In a square, all the sides are the same length.
[tex]PQ=QR=SR=SP[/tex]So, to find the length of the segment SR you can find the length of the segment QR using the formula of the distance between two points, that is:
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2^{}} \\ \text{ Where d is the distance between two points } \\ A(x_1,y_1)\text{ and} \\ B(x_2,y_2) \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} Q(7,0) \\ R(5,-8) \\ d=\sqrt[]{(5_{}-7)^2+(-8-0)^2} \\ d=\sqrt[]{(-2)^2+(-8)^2} \\ d=\sqrt[]{4+64} \\ d=\sqrt[]{68} \end{gathered}[/tex]Therefore, the length of the segment SR is
[tex]\sqrt[]{68}[/tex]10 ex 9 10 ex 3 simplified
ANSWER
[tex]10^6[/tex]EXPLANATION
We want to simplify the fraction below:
[tex]\frac{10^9}{10^3}[/tex]When you have a fraction of powers and the numerator and denominator have the same base (e.g. 10 in this case), the power on the denominator is subtracted from the power of the numerator.
So, that is:
[tex]\begin{gathered} 10^{9-\text{ 3}} \\ =>10^6 \end{gathered}[/tex]That is the answer.