since 349 can be also written as 300+40+9
write the number like so in the multiplication
[tex]6\cdot349=6\cdot(300+40+9)[/tex]apply the distributive property
[tex](6\cdot300)+(6\cdot40)+(6\cdot9)[/tex]What is the total number of college student round your answer to the nearest million
EXPLANATION:
From the data provided, 46% of all college students were enrolled part-time.
We also know that this percentage is represented by 7.8 million students. If the total number of students is given as x, then we can derive the following equation;
[tex]Total=\begin{cases}46\text{\%=7.8m} \\ 100\text{\%=x} \\ \square\end{cases}[/tex][tex]\frac{7.8}{46}=\frac{x}{100}[/tex]Cross multiply the above equation and you'll have;
[tex]\begin{gathered} \frac{7.8\times100}{46}=x \\ 16.9665=x \\ \text{Rounded to the nearet million, } \\ x\approx17 \end{gathered}[/tex]ANSWER:
The total number of students (rounded to the nearest million) therefore is 17 million.
Martina used a total of 4 3/4 gallons of gas while driving her car. Each hour she was driving, she used 5/6 gallons of gas. What was the total number of hours she was driving?
The number of hours she was driving = 5.7 hours or in fraction 57/10 hours.
What is fraction?
A fraction is a number that represents a part of a whole.
Generally, the fraction can be a portion of any quantity out of the whole thing and the whole can be any specific things or value.
Given, a total gallons is in mixed fraction 4 3/4
can be written as
16+3/4 = 19/4
Let x be the hours she was driving.
The she used 5/6 gallons.
x (5/6) = 19/4
x = 19/4(6/5)
x = 5.7 hours
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First blank transitive propertySubtraction property of equalitySegment additionSubstitution property of equalitysecond blank AB does not equal YZ AC does not equal XZ AB equals YZ AC equals XZ
Given that:
[tex]BC=XY[/tex][tex]AB+BC\ne YZ+XY[/tex]According to the Segment Addition if B lies between A and C, then:
[tex]AB+BC=AC[/tex]In this case, knowing that:
[tex]AB+BC\ne YZ+XY[/tex]And knowing that B lies between A and C, and Y lies between X and Z:
[tex]\begin{gathered} AB+BC=AC \\ YX+XY=XZ \end{gathered}[/tex]Therefore, you can determine that:
[tex]AC\ne XZ[/tex]Hence, the answers are:
- First blank: Third option (Segment addition).
- Second blank: Second option (AC does not equal XZ).
The product of two factors is x2 – X – 20. If one of the factors is x-5, what is the other factor?
we can rewrite the statement
[tex](x-5)(A)=x^2-x-20[/tex]where A is the missing factor, A must be of the form
[tex](x+a)[/tex]where a is a constant, to obtain "a" we must bear in mind that the multiplication of the two constants must give us the third term and the sum of these must give us the second term
so
[tex]\begin{gathered} -5\times a=-20 \\ -5+a=-1 \end{gathered}[/tex]if we solve any equation, the value of a is 4
so a is 4 and the factor is
[tex](x+4)[/tex][tex](x-5)(x+4)=x^2-x-20[/tex]Thelma performed a construction on a quadrilateral.Her work is shown below..EBсDWhich statement is justified by her construction?AD – AEAE - BEAD – BCO ADAD ~ DC
Looking at the image, we can see that the arc created in point E was created with the same radius of segment AD (that is, A is the center of a circle that contains both arcs that pass through points D and E).
From that construction, we can affirm that segments AD and AE are congruent.
Therefore the correct option is the first one.
Mrs. Cavazos car traveled 192 miles on 6 gallons of gas. Find the unit rate per gallon
To find the unit rate per gallon, we are going to divide 192 by 6
[tex]\frac{192}{6}=32[/tex]The car gets 32 miles per gallon.
Can you please help me find the area? Thank you. :)))
The figure shown in the picture is a rectangular shape that is missing a triangular piece. To determine the area of the figure you have to determine the area of the rectangle and the area of the triangular piece, then you have to subtract the area of the triangle from the area of the rectangle.
The rectangular shape has a width of 12 inches and a length of 20 inches. The area of the rectangle is equal to the multiplication of the width (w) and the length (l), following the formula:
[tex]A=w\cdot l[/tex]For our rectangle w=12 in and l=20 in, the area is:
[tex]\begin{gathered} A_{\text{rectangle}}=12\cdot20 \\ A_{\text{rectangle}}=240in^2 \end{gathered}[/tex]The triangular piece has a height of 6in and its base has a length unknown. Before calculating the area of the triangle, you have to determine the length of the base, which I marked with an "x" in the sketch above.
The length of the rectangle is 20 inches, the triangular piece divides this length into three segments, two of which measure 8 inches and the third one is of unknown length.
You can determine the value of x as follows:
[tex]\begin{gathered} 20=8+8+x \\ 20=16+x \\ 20-16=x \\ 4=x \end{gathered}[/tex]x=4 in → this means that the base of the triangle is 4in long.
The area of the triangle is equal to half the product of the base by the height, following the formula:
[tex]A=\frac{b\cdot h}{2}[/tex]For our triangle, the base is b=4in and the height is h=6in, then the area is:
[tex]\begin{gathered} A_{\text{triangle}}=\frac{4\cdot6}{2} \\ A_{\text{triangle}}=\frac{24}{2} \\ A_{\text{triangle}}=12in^2 \end{gathered}[/tex]Finally, to determine the area of the shape you have to subtract the area of the triangle from the area of the rectangle:
[tex]\begin{gathered} A_{\text{total}}=A_{\text{rectangle}}-A_{\text{triangle}} \\ A_{\text{total}}=240-12 \\ A_{\text{total}}=228in^2 \end{gathered}[/tex]The area of the figure is 228in²
What is the perimeter of the isosceles triangle ABC such that angle A= angle C ?
Given angle A=angle C.
The objective is to find the perimeter of the isosceles triangle ABC.
First let's find the value of x.
An isosceles triangle contains two equal sides. Here angle A and angle C are equal. So the sides AB and AC are equal.
[tex]\begin{gathered} AB=BC \\ 5x-1=3x+11 \\ 5x-3x=11+1 \\ 2x=12 \\ x=\frac{12}{2} \\ x=6 \end{gathered}[/tex]Now, find the perimeter of the triangle by adding all the sides of the triangle.
[tex]P=5x-1+3x+11+x+19[/tex]Substittue the value of x =6.
[tex]\begin{gathered} P=5(6)-1+3(6)+11+6+19 \\ P=30-1+18+11+6+19 \\ P=83 \end{gathered}[/tex]Hence, the perimeter of the triangle is 83.
[tex]\begin{gathered} \text{Let's check the whether the obtained x value if correct.} \\ AB=BC \\ 5x-1=3x+11 \\ 5(6)-1=3(6)+11 \\ 30-1=18+11 \\ 29=29 \end{gathered}[/tex]Thus the sides of isoscles triangles are equal. Hence the value of x is correct.
Working with special triangles. Find y. I have attached the picture.
In this case, we'll have to carry out several steps to find the solution.
Step :
Data:
diagram:
right triangle
Step 02:
special right triangles:
we must analyze the triangle to find the solution.
special right triangle example:
right triangle:
side y:
[tex]\begin{gathered} 88\text{ = }\sqrt{2}y\text{ } \\ \\ \frac{88}{\sqrt{2}}\text{ = y} \end{gathered}[/tex]That is the full solution.
The distances between Centerville, Springfield, and Capital City form a right triangle. The distance between Centerville and Springfield is 913 kilometers and the distance between Springfield and Capital City is 976 kilometers. View the map.
Answer:
The distance between Centerville and Capital City is 1336 kilometers.
Step by step explanation:
To solve the situation, we can use the Pythagorean theorem, which is represented by the following expression and diagram:
Now, if a=913 kilometers and b=976 kilometers. Solve for c:
[tex]\begin{gathered} 913^2+976^2=c^2 \\ c=\sqrt[]{913^2+976^2} \\ c=\sqrt[]{833569+952576} \\ c=\sqrt[]{1786145} \\ c=1336\text{ kilometers} \end{gathered}[/tex]Fill in the blanks in the sequence _,29,_,_,_,539, 1083
we are given the following sequence:
[tex]_{}29,,,,539,1083[/tex]To go from 539 to 1083 we multiply 539 by 2 and add 5, like this:
[tex]1083=539\times2+5[/tex]Therefore, for a number in position "n", the formula for its value is:
[tex]a_n=2a_{n-1}+5[/tex]Solving we get:
[tex]a_{n-1}=\frac{a_n-5}{2}[/tex]Replacing the current value for 539 we get:
[tex]a_5=\frac{a_6-5}{2}[/tex][tex]a_5=\frac{539-5}{2}=267[/tex]Now to find the 4th value:
[tex]a_4=\frac{a_5-5}{2}[/tex]Replacing:
[tex]a_4=\frac{267-5}{2}=131[/tex]For the third value:
[tex]a_3=\frac{a_4-5}{2}[/tex]Replacing:
[tex]a_3=\frac{131-5}{2}=63[/tex]The second value is already given as 29, therefore, the first value is:
[tex]a_1=\frac{a_2-5}{2}[/tex]Replacing:
[tex]a_1=\frac{29-5}{2}=12[/tex]Therefore, the sequence is:
[tex]12,29,63,131,267,539,1083[/tex]
What do all the points on this line have in common?
B. The points have an x-coordinate in common.
C. The general equation of a vertical line is x = c, where c is a constant.
Jada bought an art kit with 50 colored pencils. She and her 3 sisters will share the pencils equally. How many pencils will each person receive? Will there be any pencils left over? If so, how many?
Each will get 16 coloured pencils and 2 will be the left over
Step-by-step explanation:
Give 10 pencil each then add 6 more for each one and the answer will be 16 each and multiple 3×16 =48 and remainder 2
Pryz is a rhombus. If RK=5, RY=13 and M
Remember that
In a Rhombus
All sides are equal
Diagonals bisect each other perpendicularly
so
Part 22
Find out KY
In the right triangle RYK
Applying the Pythagorean Theorem
RY^2=RK^2+KY^2
substitute given values
13^2=5^2+KY^2
KY^2=13^2-5^2
KY^2=144
KY=12
Part 23
Find out PK
Remember that
Diagonals bisect each other perpendicularly
that means
PK=KY=12
Part 24
mRemember that
Diagonals bisect each other perpendicularly
so
mthat means
m
Part 25
mwe have that
mtherefore
m
Pieter sailed his sailboat 1,260 yards in 30 minutes . What is the average number of yards of yards he traveled per minute ? A. 21 B. 30 C. 42
Given:
Distance Pieter sailed = 1260 yards
Time taken to sail = 30 minutes
Let's solve for the average number of yards he traveled per minute.
To find the average number of yards he traveled per minute, apply the formula:
[tex]\begin{gathered} A=\frac{\text{distance in yards}}{time\text{ in minute}} \\ \\ A=\frac{1260}{30}\frac{\text{yards}}{\text{minutes}} \\ \\ A=42\text{ yards per minute} \end{gathered}[/tex]Therefore, the average number of yards he traveled per minute is 42 yards per minute.
ANSWER:
C. 42
. Connect to Everyday Life In which situation is
a rounded number appropriate? Explain.
The number of
birds in a flock
The number of players on a
football field during a game
The situations that a rounded number is appropriate is both the given situations.
The number of birds in a flock.
The number of players on a football field during a game.
Both the give situation is correct.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The number of birds in a flock.
This will always be a rounded number.
We never say that there are 3.3 birds in a flock
We always say that there are 33 birds in the flock.
The number of players on a football field during a game.
This is always a rounded number.
We never say that there are 3 and a half players or 4.5 players on a football field.
We always say 24 players on a football field.
Thus,
The situations that a rounded number is appropriate is both the given situations.
The number of birds in a flock.
The number of players on a football field during a game.
Both the given situation is correct.
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Answer:
The situations that a rounded number is appropriate is both the given situations.The number of birds in a flock.The number of players on a football field during a game.Both the give situation is correct.What is an expression?An expression is a way of writing a statement with more than two variablesor numbers with operations such as addition, subtraction, multiplication, and division.Example: 2 + 3x + 4y = 7 is an expression.We have,The number of birds in a flock.This will always be a rounded number.We never say that there are 3.3 birds in a flockWe always say that there are 33 birds in the flock.The number of players on a football field during a game.This is always a rounded number.We never say that there are 3 and a half players or 4.5 players on a football field.We always say 24 players on a football field.
true or false the diameter is equal to twice the radius
True, the diameter = twice the radius
KFind the future value and interest earned if $8806.54 is invested for 7 years at 4% compounded (a) semiannually and (b) continuously.(a) The future value when interest is compounded semiannually is approximately $ 11,620.04.(Type an integer or decimal rounded to the nearest hundredth as needed.)The interest earned is approximately $ 2813.5.(Type an integer or decimal rounded to the nearest hundredth as needed.)(b) The future value when interest is compounded continuously is approximately $(Type an integer or decimal rounded to the nearest hundredth as needed.)
Given:
The principal amount = $8806.54
Rate of interest = 4%
Time = 7 years
Required:
Find the future value when interest is compounded continuously.
Explanation:
The future value is calculated by using the formula:
[tex]Future\text{ value = Ae}^{rt}[/tex]Where A = amount
r = rate of interest
t = time period
Substitute the given values in the formula:
[tex]\begin{gathered} Future\text{ value = 8806.54\lparen e}^{0.04\times7}) \\ =8806.54(e^{0.28}) \\ =8806.54\times1.323 \\ =11,651.0524 \\ \approx11,651.05 \end{gathered}[/tex]Interest = 11,651.05 - 8806.54
= 2844.51
Final Answer:
The future value when interest is compounded continuously is approximately $11,651.05.
The earned interest is approximately $2844.51
what is the median 14,6,-11,-6,5,10
The median of a set of values is the values that divide the set into two subsets, one containing all the values less than the median, and another containing all the values greater than the median.
So, to find the median, let's first rewrite the given values in ascending order:
-11, -6, 5, 6, 10, 14
If the set had an odd number of values, the value in the middle, after rewriting them as we did, would be the median.
Nevertheless, the number of values in this set is even. When this happens, the median corresponds to the mean of the two central numbers.
In this case, the two central numbers are 5 and 6. Their mean is:
(5 + 6)/2 = 11/2 = 5.5
Thus, the median is 5.5.
A bottler of drinking water fills plastic bottles with a mean volume of 993 milliliters (mL) and standard deviation of 7 mL. The fill volumes are normally distributed. What proportion of bottles have volumes between 988 mL and 991 mL?
Given data:
Mean: 993mL
Standard deviation: 7mL
Find p(988
1. Find the z-value corresponding to (x>988), use the next formula:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \\ z=\frac{988-993}{7}=-0.71 \end{gathered}[/tex]2. Find the z-value corresponding to (x<991):
[tex]z=\frac{991-993}{7}=-0.29[/tex]3. Use a z score table to find the corresponding values for the z-scores above:
For z=-0.71: 0.2389
For x=-0.29: 0.3859
4. Subtract the lower limit value (0.2389) from the upper limit value (0.3859):
[tex]0.3859-0.2389=0.147[/tex]5. Multiply by 100 to get the percentage:
[tex]0.147*100=14.7[/tex]Then, 14.7% of the bottles have volumes between 988mL and 991mLSolve x2 + 5x = 0.Step 1. Factor x2 + 5x as the product of two linear expressions.
Taking common factor x:
[tex]x(x+5)=0[/tex]Equal each factor to zero, and solve for x:
[tex]x=0[/tex][tex]\begin{gathered} x+5=0 \\ x=-5 \end{gathered}[/tex]So, the solution is:
[tex]\begin{gathered} x_1=0 \\ x_2=-5 \end{gathered}[/tex]the equation below describe the graph of a line on a coordinate planes.y - 2 = -3/2 (x + 1) which graph represents this line ?
The y-intercept is 1/2.
The answer is C. we can use the y-intercept to know the graph. You can see that option C when x = 0 , y is 1/2.
Find the image of the given pointunder the given translation.
Answer: P' = (4, 4)
Explanation
As the given point is (8, –3), then the transformation is:
[tex]T(x,y)=(x-4,y+7)=(8-4,-3+7)[/tex][tex]T(x,y)=(4,4)[/tex]|- 1/5| ? |-0.8|what’s the missing inequality symbol?
Given:-
[tex]|-1\frac{1}{5}|,|-0.8|_{}[/tex]To find the correct inequality between the given datas.
So now we simplify. so we get,
[tex]|-1\frac{1}{5}|=|-\frac{6}{5}|=|-1.2|[/tex]So we get,
[tex]\begin{gathered} |-1.2|=1.2 \\ |-0.8|=0.8 \end{gathered}[/tex]So the inequality is,
[tex]1.2>0.8[/tex]Select all of the true statements about to figure, if a scale factor is 2.
Given: The scale factor is 2 for the given figures
To Determine: The truth statements from the given options
The transformation shown is an enlargement. This means that each of the length of the pre-image multiplied by 2 would give the length of the image
This means
[tex]\begin{gathered} A^{\prime}B^{\prime}=2AB \\ A^{\prime}C^{\prime}=2AC \\ B^{\prime}C^{\prime}=2BC \end{gathered}[/tex]For similar shapes, the angles are congruent and the sides are in proportion of the scale factor
Hence, the following are true statements of the given diagrams
A'C' = 2 AC, OPTION B
If AB = 6, then A'B' = 12, OPTION E
Ann, justin, and kevin sent a total of 88 text message during the weekend. Ann sent 8 more message than justin. kevin sent 3 times as many message as justin. how many message did they each send
let the no. of message sent by Ann is A,
the no. of the message sent by Justin is J
the no. of the message sent by Kevin is K
sum of messages is = 88
A + J + K = 88
it is given that Ann sent 8 more messages than justiJustinn.
A = J + 8
Kevin sent 3 times as many as Justin.
K = 3 J
substitute all the values ,
(J + 8 ) + J + ( 3 J) = 88
5J + 8 = 88
5J = 88 - 8
5J = 80
J = 80/5
J = 16
messages sent by Ann is A = J + 8 = 16 + 8 = 24 message
messages sent by Ann is 24 messages
messages sent by Justin is J = 16 message
messages sent by Justin is 16 messages
messages sent by Kevin is K = 3J = 3 x 16 = 48 message
messages sent by Kevin is 48 message.
question will be in picture
f(x) = -5x + 4
What is the value of x when f(x) = 29
To find x, equate -5x + 4 to 29.
-5x + 4 = 29
Next, collect like terms.
-5x = 29 - 4
-5x = 25
Finally divide through by -5 to find the value of x.
[tex]\begin{gathered} \frac{-5x}{-5}\text{ = }\frac{25}{-5} \\ x\text{ = -5} \end{gathered}[/tex]Final answer
x = -5 Option C
I need help solving this logarithmic equation. I need answered step by step,
Okay, here we have this:
We need to solve the following equation for n:
[tex]\log _8n=3[/tex]To solve this equation we will pass the logarithm to its exponential form:
[tex]\begin{gathered} n=8^3 \\ n=8\cdot8\cdot8 \\ n=512 \end{gathered}[/tex]Finally we obtain that n=512.
Answer:
n = 512
Step-by-step explanation:
Solving logarithmic equations:Write logarithmic equations to exponential equation.
[tex]\sf \log_8 \ n = 3\\\\\\ 8^3 = n\\\\[/tex]
n = 8 * 8 *8
n = 512
In triangle ABC, AB12, BC18, and m B = 75°. What are the approximate length of AC and measure of A
Length AB = 12cm
BC = 18cm
mB = 75^
a triangle has side lengths of 6,7, and 14 is it possible or impossible
Answer:
Impossible
Explanation:
The side lengths a, b and c can form a triangle if the inequality holds:
[tex]a+b\ge c[/tex]Given the side lengths 6,7 and 14:
[tex]\begin{gathered} 6+7=13\le14\text{ (This invalidates it)} \\ 6+14=20\ge7 \\ 6+13=19\ge7 \end{gathered}[/tex]Since the inequality does not hold in all cases, it is Impossible to form sides of a triangle.