The given numbers are
5.78 x 10^5 and 8.04 x 10^-2
We would simplify the exponents by applying one of the laws of exponents which states that
a^b x a^c = a^(b + c)
By applying this law, the expression becomes
5.78 x 8.04 x 10^(5 + - 2)
46.4712 x 10^(5 - 2)
46.4712 x 10^3
The product in scientific notation is
46.4712 x 10^3
A certain drug is made from only two ingredients: compound A and compound B. There are 5 milliliters of compound A used for every 7 milliliters of compound B. If a chemist wants to make 1056 milliliters of the drug, how many milliliters of compound A are needed?what is the answer?
If the proportion of compounds A and B is 5 to 7, we can calculate the amount of each compound in the total of 1056 using the equations:
[tex]\begin{gathered} A=\frac{5}{5+7}\cdot1056 \\ A=\frac{5}{12}\cdot1056 \\ A=440 \\ \\ B=\frac{7}{5+7}\cdot1056 \\ B=\frac{7}{12}\cdot1056 \\ B=616 \end{gathered}[/tex]So the amount of compound A needed is 440 ml.
Why is the product of two rational numbers always rational?Select from the drop-down menus to correctly complete the proof. Let ab and cd represent two rational numbers. This means a, b, c, and d are Choose... integers or irrationals number , and b and d are not 0. The product of the numbers is acbd, where bd is not 0. Both ac and bd are Choose... integers or irrationals numbers, and bd is not 0. Because acbd is the ratio of two Choose... integers or irrationals numbers, the product is a rational number.
a rational number is a type of real numbers, which is in the form of p/q where q is not equal to zero.
Let a/b and c/d represent two rational numbers. This means a, b, c, and d are integers, and b and d are not 0. The product of the numbers is ac/bd, where bd is not 0. Both ac and bd are integers, and bd is not 0. Because ac/bd is the ratio of two integers, the product is a rational number
Tina has earned a total of 9,644 frequent flyer miles by traveling between twin falls and Preston. she has made 4 trip time how many miles is one trip between thses to city's.
it is given that total miles travelled by tine are 9644 miles in the four trips.
now we calculate the distance travelled in one trip by tina,
[tex]\frac{9644}{4}=2411\text{ miles}[/tex]so tina travels 2411 miles in one trip.
An electric guitar costs $790, with a $235 full-replacement warranty. If the manufacturer sells 598,274 warranties andhas to honor 11% of them, how much profit did the manufacturer gain from the warranties? Show work
Frank and Erica are selling ribbons to raise money for the football team. The graph shows the linear relationship between the number of ribbons each of them has left to sell and the number of days that they have been selling ribbon
Notice how both lines intersect at 18 days. That means that at that point in time, both lines represent a value that is exactly the same.
Therefore, Frank and Erica will have the same to sell on Day 18
(Option J)
Which geometric formulas describe functions that are nonlinear? Select all that apply. (A) P=3s 6) A=65² C) d=2r D C= 2tr E 4. V=
Answer:
B. A = 6s²
E. V = (4/3)πr³
Explanation:
A formula describes a function that is nonlinear if the exponent of the variable is greater than 1.
Therefore, the geometric formulas that describe functions that are nonlinear:
A = 6s²
V = (4/3)πr³
Because the variable s has an exponent equal to 2 for the first one and the variable r has an exponent equal to 3 for the second one.
The distribution of the binomial random variable (x) has the following parameters: p = 0.3 and n = 9 Determine the P(X ≥ 2)
Answer:
Explanation:
The formula for calculating binomial probability is expressed as
P(x) = nCx * p^x * q^(n - x)
where
n is the number of trials
x is the number of successes
p is the probability of success
q is the probability of failure
From the information given,
n = 9
p = 0.3
q = 1 - p = 1 - 0.3 = 0.7
By using a binomial probability calculator,
P(x ≥ 2) = 0.804
what us the value of x that makes the equation true?
find the equations of the line those pass through (2/3, -3/5) and have slope 5/3
Slope intercept form (general)
y = mx + b
Where:
m= slope
b= y-intercept
m = 5/3
y = 5/3x + b
Replace ( x,y ) by the given point (2/3,-3/5) and solve for b.
-3/5 = 5/3 (2/3) + b
-3/5 = 10/9 + b
-3/5 - 10/9 = b
b = -77/45
y = 5/3x - 77/45
I have a calculus one question about derivatives as rates of change when it comes to population picture included
Okay, here we have this:
Considering the provided information, we are going to calculate the requested population, so we obtain the following:
Let us remember that we are talking about linear growth, therefore we will solve for the following formula:
[tex]\begin{gathered} f(x)=b+mx \\ 68000=17000+m(2) \\ 51000=2m \\ m=\frac{51000}{2} \\ m=25500 \end{gathered}[/tex]Now, let's calculate the population after one year:
[tex]\begin{gathered} f(x)=17000+25500x \\ f(1)=17000+25500(1) \\ f(1)=17000+25500 \\ f(1)=42500 \end{gathered}[/tex]Finally we obtain that after one year the population will be 42500.
There are 48 employees in a company. On a certain day, 36 were present. What percent showed up for work'
Answer:
75%
Step-by-step explanation:
Divide 48 by 36:
36/48=
(12*3)/(12*4)=
3/4=0.75
Multiply the decimal by 100 to get the percent:
0.75*100=75%
The workers present on the certain day given is 75%
What is percentage?A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.
Given that, There are 48 employees in a company. On a certain day, 36 were present.
To find the percentage of workers present = present/totalx100
= 36/48x100
= 75
Hence, The workers present on the certain day given is 75%
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A ferris wheel has a radius of 65 feet. How many feet will the feris wheel have turned after 10 rotations.
we need to calculate the perimeter of a circle of radius 65
perimeter=2pi*radius=2pi*65=130pi
then after 10 rotations the wheel have turned 10(130pi) feets= 1300pi feets
Use the point-slope formula to write an equation of the line that passes through (-3, 2) and (-6, -2).Write the answer in slope-intercept form (if possible).
The equation of a line in the slope-intercept form is y = mx + b, where "m" is the slope and b is the y-intercept.
To find the equation of the line given two points (x, y), follow the steps below.
Step 01: Substitute the point (-3, 2) in the equation.
To do it, substitute x by -3 and y by 2.
[tex]\begin{gathered} 2=m\cdot(-3)+b \\ 2=-3m+b \end{gathered}[/tex]Isolate b by adding 3m to both sides of the equation.
[tex]\begin{gathered} 2+3m=-3m+b-3m \\ 2+3m=-3m+3m+b \\ 2+3m=b \end{gathered}[/tex]Step 02: Substitute b in the equation of the line.
Knowing that b = 2 + 3m. Then,
[tex]\begin{gathered} y=mx+b \\ y=mx+2+3m \end{gathered}[/tex]Step 03: Substitute the point (-6, -2) in the equation from step 02.
To do it, substitute x by -6 and y by -2.
[tex]\begin{gathered} -2=m\cdot(-6)+2+3m \\ -2=-6m+2+3m \\ -2=-3m+2 \end{gathered}[/tex]Isolate "m" by subtracting 2 from both sides.
[tex]\begin{gathered} -2-2=-3m+2-2 \\ -4=-3m \end{gathered}[/tex]Finally, divide both sides by -3:
[tex]\begin{gathered} \frac{-4}{-3}=\frac{-3}{-3}m \\ \frac{4}{3}=m \end{gathered}[/tex]Knowing "m", use the equation from step 1 to find "b".
Step 04: Find "b".
[tex]\begin{gathered} b=2+3m \\ \end{gathered}[/tex]Substituting m by 4/3 and solving the equation:
[tex]\begin{gathered} b=2+3\cdot\frac{4}{3} \\ b=2+\frac{3\cdot4}{3} \\ b=2+4 \\ b=6 \end{gathered}[/tex]Answer: The equation of the line is:
[tex]y=\frac{4}{3}x+6[/tex](-9,-5),(-6,1) and (5,8)What is the perimeter?
Answer
The perimeter of the triangle is 48.298 units
Explanation
The triangle has the vertices (-9, -5), (-6, 1) and (5, 8).
To find the perimeter of the triangle, we need to find the lengths of the sides of the triangle. The perimeter is the sum of all its sides.
Each side will be calculated from the distance between the vertices.
The distance between two points with the coordinates (x₁, y₁) and (x₂, y₂) is given as
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
The sides of the triangle will be between
(-9, -5) and (-6, 1)
(-9, -5) and (5, 8)
(-6, 1) and (5, 8)
(x₁, y₁) and (x₂, y₂) is (-9, -5) and (-6, 1)
x₁ = -9
y₁ = -5
x₂ = -6
y₂ = 1
d = √[(-6 - (-9))² + (1 - (-5))²]
d = √[(-15)² + (6)²]
d = √(261)
d = 16.155
(x₁, y₁) and (x₂, y₂) is (-9, -5) and (5, 8)
x₁ = -9
y₁ = -5
x₂ = 5
y₂ = 8
d = √[(5 - (-9))² + (8 - (-5))²]
d = √[(14)² + (13)²]
d = √(365)
d = 19.105
(x₁, y₁) and (x₂, y₂) is (-6, 1) and (5, 8)
x₁ = -6
y₁ = 1
x₂ = 5
y₂ = 8
d = √[(5 - (-6))² + (8 - 1)²]
d = √[(11)² + (7)²]
d = √(170)
d = 13.038
The perimeter of the triangle is thus given as
Perimeter = 16.155 + 19.105 + 13.038
= 48.298 units
Hope this Helps!!!
Billy is solving the inequality 4x - 4 > 20:His work is shown:4x - 4 > 20+4+44x > 244 4X < 6Did Billy solve the problem correctly? If not, where did Billy make a mistake
He added 4 to both sides:
[tex]\begin{gathered} 4x-4+4>20+4 \\ 4x>24 \end{gathered}[/tex]He divided both sides by 4:
[tex]\begin{gathered} \frac{4x}{4}>\frac{24}{4} \\ x>6 \end{gathered}[/tex]However he got:
x < 6
He flipped the inequality sign which is incorrect since he is not dividing by a negative number
What steps do you take in order to construct an equilateral triangle using a compass and a straight edge?
An equilateral triangle is one that has three equal sides, therefore it is more importante than with the rule to create 3 sides of the same length.
What is the slope of a line that is parallel to the line y = 3/4x + 2?
-4/3
-3/4
3/4
4/3
Answer:
The slope of this line is 3/4.
point (0,6) in which quadrant and axis
Given the point:
(0, 6)
Let's find the quadrant and the axis where the point is located.
We have:
(x, y) ==> (0, 6)
The x-coordinate of the point is 0, while the y-coordinate of the point is 6.
Here, the point (0, 6) lies on the y-axis.
Also, since the x-coordinate is 0, we can say the point lies in between quadrant I and quadrant II.
From the graph above we can see the point (0, 6) is between quadrant I and II, and the point lies on the y-axis.
ANSWER:
• The point is in beween Quadrant I and II
,• The point lies on the y-axis.
Tyler se comió x bocadillos de frutas, y Han comió m menos que eso. Escribe una expresión para la cantidad de bocadillos de frutas que comió Han.
the expression
[tex]x-m[/tex]represents the amount of snacks Han ate.
The ratio of the measures of the three angles in a triangle are 3:4:6. Determine the measures of each angle of the triangle.
Given:
The ratio of the angles is 3:4:6.
Required:
We need to find the measure of each angle of the triangle.
Explanation:
Let the angles of the triangle be 3x, 4x and 6x.
We know that the sum of the angles is equal to 180 degrees.
[tex]3x+4x+6x=180\degree[/tex][tex]13x=180\degree[/tex]Divide both sides by 13.
[tex]\frac{13x}{13}=\frac{180\degree}{13}[/tex][tex]x=13.85[/tex]Substitute x values in 3x, 4x and 6x.
[tex]3x=3\times13.85=41.55[/tex][tex]4x=4\times13.85=55.4[/tex][tex]41.55+55.4+6x=180[/tex][tex]6x=83.05[/tex]Final answer:
The angles are 41.55, 55.40 and 83.05.
Complete the sentence below. A rhombus is a rectangle. always sometimes never Submit
The correct answer is Never
Perform the indicated operation and express the result as a simplified complex number in the form a+bi. Do not put any spaces between your characters.(-2-4i)+(1+6i)simplifies to Answer
Given the expression:
(-2 - 4i) + (1 + 6i)
Let's simplify the expression.
To simplify the expression, let's combine the real and imaginary parts.
• Remove the parentheses:
[tex]-2-4i+1+6i[/tex]• Combine the like terms:
[tex]\begin{gathered} -2+1-4i+6i \\ \\ -1+2i \end{gathered}[/tex]ANSWER:
[tex]-1+2i[/tex]Select all the equations on which the point (10,0) lies. O 5x + 2y = 15 O 2x + 4y = 20 O x + y = 10 O 3x + 3y = 13 4x + 2y = 20 O 6x + y = 50
2x + 4y = 20
when y = 0
2x + 4(0) = 20
2x = 10
Divide both-side of the equation by 2
x = 10
Hence, it lies on the point 2x + 4y = 20
Find AB. A =20B = 10C = 54 D = 12
Answer:
C. 54
Explanation:
The triangles ABD and ACD are congruent by SAS (Side - angle - side) becuase
AD is congruent to itself
∠ADB = ∠ADC
BD is congruent to CD
So, the length of AB is equal to the length of AC and we can write the following equation
AB = AC
4x + 6 = 5x - 6
Solving for x, we get:
4x + 6 + 6 = 5x - 6 + 6
4x + 12 = 5x
4x + 12 - 4x = 5x - 4x
12 = x
Then, the length of AB is
AB = 4x + 6
AB = 4(12) + 6
AB = 48 + 6
AB = 54
Therefore, the answer is
C. 54
7. Tres hermanos tienen una bolsa de golosinas. Quieren regalarle a su padre un trozo de twizzler cada uno. Si cada trozo de twizzler que regalan tienen 100 mm, ¿cuántos centímetros de twizzler tendrá en total el padre?
Como cada uno de los hermanos le regalará un trozo de twizzler a su padre, ékl tendra tres twizzlers. En milímetros eso es
[tex](3)(100)=300\text{ mm}[/tex]Ahora tenemos que convertir los milimetros a centímetros. Recordemos que un centímetro tiene 10 milímetros. Entonces, tenemos que dividir la cantidad total de milímetros entre 10.
[tex]\frac{300}{10}=30[/tex]Por lo tanto el padre tendrá 30 cm de twizzler en total.
Write the factored form of the least common denominator needed to simplify this expression.9419 + 3+g2 + 29- 15+5
ANSWER
[tex]g^2+2g-15=(g+5)(g-3)[/tex]EXPLANATION
Given:
[tex]\frac{g+1}{g^2+2g-15}+\frac{g+3}{g+5}[/tex]Desired Outcome:
The factored form of the least common denominator
Simplify the expression
[tex]undefined[/tex]Question 10 of 25Which of the following are roots of the polynomial function below?Check all that apply.F(x) = 2x³-²-9x+6OA. 9-√55B. 2□ C. -3-√33D.9+√√554-3+√33E.SUBMIT
Given
F(x) = 2x³-²-9x+6
Find
roots of the polynomial function below
Explanation
we have to find the roots of the polynomial function.
[tex]\begin{gathered} f(x)=2x^3-x^2-9x+6 \\ f(x)=(x-2)(2x^2+3x-3) \end{gathered}[/tex]now solve quadratic equation ,
[tex]\begin{gathered} 2x^2+3x-3=0 \\ \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ x=\frac{-3\pm\sqrt{(3)^2-4\times2\times(-3)}}{4} \\ \\ x=\frac{-3\pm\sqrt{9+24}}{4} \\ \\ x=\frac{-3\pm\sqrt{33}}{4} \end{gathered}[/tex]Final Answer
Therefore , the correct options are B , C and E
Eric and Sarah both have lemonade stands. The graph below represents how many cupsof lemonade Eric sells per day. The equation represents the rate at which Sarahmakes lemonade. Who sold more cups of lemonade in 5 days?
The graph indicates that Eric sells 60 cups of lemonade in 5 days.
Substituting x = 5 in the equation of Sarah, we get:
y = 10x
y = 10*5
y = 50
That is, Sarah sells 50 cups of lemonade in 5 days.
Then, Eric sells more cups.
Can you please answer so I already have the answers on the side if you can see but can you show me how he did it
What is 0.023% of 2100?
Word "is" means = and the word "of" means times
So it is x = 0.023% * 2100
At first, change 0.023% to a normal number by dividing it by 100
[tex]x=\frac{0.023}{100}\times2100[/tex]Let us simplify the right side
[tex]x=0.023\times21[/tex]Now use your calculator to find the answer
x = 0.483
0.483 is 0.023% of 2100
-Quadratic Equations-write a standard form Quadratic Equation with the given solution.
Answer:
x² + 49 = 0
Explanation:
An equation with the form (x - a)(x - b)= 0 has as a solutions x = a and x = b.
In this case, the solutions are x = 7i and x = -7i, so the equation will be:
(x - 7i)(x - (-7i)) = 0
(x - 7i)(x + 7i) = 0
Now, we need to apply the distributive property, so:
x(x) + x(7i) - 7i(x) - 7i(7i) = 0
x² + 7xi - 7xi - 49i² = 0
x² - 49i² = 0
Since, i² = -1, we get:
x² - 49(-1) = 0
x² + 49 = 0
Therefore, the quadratic equation in standard form is:
x² + 49 = 0
This is the standard form of the given quadratic equation is [tex]x^{2} +49=0[/tex]
Quadratic Equation-It is a type of equation in which the maximum power a variable can hold is 2 and the variable cannot be 0
The solution of the given equation are x=7i and x=-7i
we can write the equation as (x-7i)(x-(-7i))=0
as (An equation in the form of (x-a)(x-b)=0 is having x=a and x=b as their solution)
(x-7i)(x+7i)=0
According to the distributive property
(Distributive property-It states that A(B+C)=AB+AC)
x(x)+x(7i)-7i(x)-7i(7i)=0
[tex]x^{2}[/tex]+7xi-7xi-49[tex]i^{2}[/tex]=0
[tex]x^{2}[/tex]-49[tex]i^{2}[/tex] =0
since,([tex]i^{2}[/tex]=-1),we get:
[tex]x^{2}[/tex]+49=0
hence, the quadratic equation in standard form is
[tex]x^{2}[/tex]+49=0
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