Based on the mathematical statements, Zoe is 56 years old and Luke is 66 years old, now
How to determine how old they are now?From the question, we have the following statements that can be used in our computation:
30 years ago
Zoe was 2/3 as old as Luke
18 years ago
Zoe was 5/6 as old as Luke
Let their present ages be represented as
Zoe = x
Luke = y
So, we have the following representations
30 years ago
Zoe was 2/3 as old as Luke
x - 36 = 2/3(y - 36)
18 years ago
Zoe was 5/6 as old as Luke
x - 18 = 5/6(y - 18)
So, we have the following system of equations
x - 36 = 2/3(y - 36)
x - 18 = 5/6(y - 18)
Make x the subject in x - 18 = 5/6(y - 18)
x = 5/6(y - 18) + 16
Substitute x = 5/6(y - 18) + 16 in x - 36 = 2/3(y - 36)
5/6(y - 18) + 16 - 36 = 2/3(y - 36)
Open the brackets
5/6y - 15 + 16 - 36 = 2/3y - 24
Evaluate the like terms
5/6y - 35 = 2/3y - 24
Multiply through by 6
5y - 210 = 4y - 144
Evaluate the like terms
y = 66
Substitute y = 66 in x = 5/6(y - 18) + 16
x = 5/6(66 - 18) + 16
Evaluate
x = 56
Recall that
Zoe = x
Luke = y
So, we have
Zoe = x = 56
Luke = y = 66
Hence, they are 56 and 66 years, now
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The formula is у= 6х - 5 Determine the value of x, if y=7
Answer:
x=2
Step-by-step explanation:
You can put the equation as 7=6x-5
Move equation
12=6x
Divide
x=2
Over the last three evenings, Amanda received a total of 63 phone calls at the call center. The third evening, she received 2 times as many calls as the first
evening. The second evening, she received 5 fewer calls than the first evening. How many phone calls did she receive each evening?
68 calls she received in each evening .
What is linear equation ?A straight line equation and equations with a maximum order of one are referred to as "linear equations." The formula for the linear equation can be written as Y = mx + b, where m is the slope of the line, b is the y-intercept, and x and y are the variables. Slopes tell us the direction and steepness of a line. The value of y when x is 0 is referred to as the y-intercept because (0,y) is the point where the line crosses the y-axis.
CalculationLet's say the number of calls on the second night was x.
The first evening was then x+7.
The third evening she received 4x calls.
Add them up to make 109 calls....
x + x+7 + 4x = 109
6x + 7 = 109
6x = 102
x = 17 calls
x+7 = 24 calls
4x = 68 calls
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On a banquet table, 8 different dishes of food will be placed in a row. There are 4 vegetarian dishes and 4 meat dishes.
They will be placed alternating between the two types of dishes. A vegetarian dish will be first. How many ways are
there to place the dishes on the table?
If a vegetarian dish will be first. The number of different ways that are there to place the dishes on the table is 576.
How to find the number of different ways?There are 4 vegetarian dishes = P4 = 4!
There are 4 meat dishes =P4 =4!
Now let find the number of different ways
Number of different ways = 4! × 4!
Number of different ways = 24 × 24
Number of different ways = 576 different ways
Therefore the number of different ways is 576.
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Which statements are true about the ordered pair (−4, 0) and the system of equations? {2x+y=−8x−y=−4 Select each correct answer. Responses The ordered pair (−4, 0) is a solution to the first equation because it makes the first equation true. The ordered pair , begin ordered pair negative 4 comma 0 end ordered pair, is a solution to the first equation because it makes the first equation true. The ordered pair (−4, 0) is a solution to the second equation because it makes the second equation true. The ordered pair , begin ordered pair negative 4 comma 0 end ordered pair, is a solution to the second equation because it makes the second equation true. The ordered pair (−4, 0) is not a solution to the system because it makes at least one of the equations false. The ordered pair , begin ordered pair negative 4 comma 0 end ordered pair, is not a solution to the system because it makes at least one of the equations false. The ordered pair (−4, 0) is a solution to the system because it makes both equations true.
The statements that are true about the ordered pair (−4, 0) and the system of equations include the following:
The ordered pair (−4, 0) is a solution to the second equation because it makes the second equation true. The ordered pair (−4, 0) is not a solution to the system because it makes at least one of the equations false.How to determine the solution?In order to determine which statements are true with respect to a solution of the given system of linear equations, we would have to test the given ordered pairs by substituting their values into the linear equations as follows;
For ordered pair (-4, 0), we have:
2x + y = -8x
2(-4) + 0 = -8(4)
-8 = -32 (False)
For ordered pair (-4, 0), we have:
x - y = -4
-4 - 0 = -4
-4 = -4 (True).
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DONT IGNORE PLEASE HELP! Identify the correct diagram and formula to find the measure of an interior angle of hexagon.
The formula to find the measure of an interior angle of a hexagon is [(n - 2)×180]/n. Hence, option C is correct.
What is a Polygon?In geometry, a polygon is any enclosed curve made up of a collection of continuous line segments (sides) without any intersections.
Triangles (three sides), polyhedral (four sides), and pentagons are the three simplest polygons (five sides). Convex polygons are those in which none of the elongated sides overlap the polygon; concave polygons are those in which they do.
Equilateral refers to a polygon with equal angles. Equiangular shapes have equal internal angles on all sides. Regular polygons are any equilateral and equiangular polygons.
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=
Simple interest is given by the formula A P+Prt. Where A is the balance of the
account after t years, and P is the starting principal invested at an annual percentage rate
of r, expressed as a decimal.
Bill is investing $26,000 into a savings account that pays 2.6% simple interest. How long will
it take for this investment to double in value?
It will take
Round your answer to the nearest tenth.
years for this investment to double in value.
The investment will take 38.5 years to double in value.
What is simple interest?
The principal of a loan or the first deposit into a savings account serves as the basis for simple interest. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.
P=$26,000 r=2.6%=0.026
A=2P=2(26,000)=$52,000
A=P+Prt
Substitute the known values
52,000=26,000+(26,000×0.026t)
52,000-26,000=676t
On simplifying, we get t= 38.46 years
Rounded number to the nearest tenth=38.5 years
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Suppose that you have a square pyramid like the one pictured. Which plane section will produce a trapezoid? Question 4 options: A) Cutting off one of the bottom corners B) A cut parallel to the vertical axis, directly through the vertical axis C) A cross section cut parallel with the bottom D) A cut parallel to the vertical axis, but off the vertical axis
When you have a square pyramid, the plane section that will produce a trapezoid is B. A cut parallel to the vertical axis, directly through the vertical axis
What is a square pyramid?It is defined in geometry as a shape with a square base with equal side lengths and all of the square's joints at the top that are perpendicular to the center of the square.
Geometry, as we know, is the branch of mathematics concerned with the size, shape, and orientation of two-dimensional figures. A trapezoid, also known as a trapezium, is a closed, flat shape with four straight sides and one pair of parallel sides.
It's parallel sides are known as the bases, and its non-parallel sides are known as the legs. A trapezoid can have parallel legs as well.
In this case, the cut parallel to the vertical axis, directly through the vertical axis will produce the trapezoid.
In conclusion, the correct option is B.
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Which equation has the same solution as x² + 4x + 13 = -10?
From the given set of equation the one which has same solution as
x² + 4x + 13 = -10 is given by (x+2)² = -19.
As given in the question,
Given equation is equal to:
x² + 4x + 13 = -10
Simplify it we get,
x² + 4x + 13 +10 =0
⇒ x² + 4x + 23 =0 ___(1)
General quadratic equation is
ax² + bx + c =0
a = 1 , b =4 , c =23
Simplify the given options we have:
a. (x+2)² = -19
⇒ x² + 4x + 4 = -19
⇒ x² + 4x + 4 + 19 =0
⇒ x² + 4x + 23 =0
Has same solution as given one.
b. (x-2)² = -27
⇒ x² -4x + 4 +27 =0
⇒x² -4x +31 =0
'b' and 'c' value are different
Not have same solution.
c. (x-2)² =-19
⇒ x² -4x + 4 +19 =0
⇒x² -4x +23 =0
'b' value is different.
Not have same solution.
d. (x+2)² = -27
⇒ x² +4x + 4 +27 =0
⇒x² +4x +31 =0
'c' value is different
Not have same solution.
Therefore, from the given set of equation the one which has same solution as x² + 4x + 13 = -10 is given by (x+2)² = -19.
The complete question is:
Which equation has the same solution as x² + 4x + 13 = -10?
a. (x+2)² = -19
b. (x-2)² = -27
c. (x-2)² =-19
d. (x+2)² = -27
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Find two z values so that the middle 67% of the area is bounded by them.
The two z values that the middle 67% of the area is bounded by them are -3.999 and 3.999.
What is a standard normal distribution?In all continuous probability distributions, it is possible to calculate the percentiles, which are defined as the value of the random variable that leaves an area equal to the percentile to the left of the distribution. When it comes to a central percentile, the area is distributed and the percentile is determined using a table of values or technology.
The area between the two boundaries is 0.67and the remaining area is 0.33 (= 1-0.56) , which is to the left of it.
Look into the z table to find the area between z=-x and mean and z=x and mean. According to z score table z=0.44 has 0.67 of the area to the left of (below) it. That means z=-0.44 has 0.67 of the area to the right of (above) it.
Therefore, the two z values are 0.44 and -0.44.
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The two z values that the middle 67% of the area is bounded by them are -3.999 and 3.999.
What is a standard normal distribution?In all continuous probability distributions, it is possible to calculate the percentiles, which are defined as the value of the random variable that leaves an area equal to the percentile to the left of the distribution. When it comes to a central percentile, the area is distributed and the percentile is determined using a table of values or technology.
The area between the two boundaries is 0.67and the remaining area is 0.33 (= 1-0.56) , which is to the left of it.
Look into the z table to find the area between z=-x and mean and z=x and mean. According to z score table z=0.44 has 0.67 of the area to the left of (below) it. That means z=-0.44 has 0.67 of the area to the right of (above) it.
Therefore, the two z values are 0.44 and -0.44.
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4. A Space Z engineer is testing the design of a new heat shield for its Komodo spacecraft. The design is meant to prevent
the interior of the shield from reaching a temperature of 200◦C. Over the course of 24 trials, the average temperature
of the shield was 194.37◦C with a standard deviation of 4.29◦C. Assume all temperature measurements follow a normal
distribution.
(a) Test at the 1% level of significance if the shield’s average temperature is less than 200◦C.
(b) Explain a Type I error in the context of the data.
At the 1% level of significance, the heat shield for the Komodo spacecraft have average temperature of 191.811° C < x-bar < 196.73° C which is less 200◦C
Type I error is explained below
How to know of the shield's average temperature is less than 200 degree Celsius1% level of significance means that the p value or the probability of the temperature of the new heat shield for Komodo spacecraft being less than 200° C is less than 1%
The range of average temperatures of the shield is given by the formula
= x-bar ± t(s/√n)
Definition of variables
mean, x-bar = 194.37° C
standard deviation, s = 4.29° C
sample size, n = 24
significance level = 1%
confidence level = 1 - significance level = 1 - 0.01 = 0.99 = 99%
z score, z
For sample size less than 30, n < 30. t scores are used
degree of freedom, df = n - 1 = 24 - 1 =23
t score for 99% confidence level and df of 23 = 2.808
substituting into the formula
= x-bar ± t(s/√n)
= 194.37 ± 2.808 (4.29/ √24)
= 194.27 ± 2.4589
= 191.811 ° C < x-bar < 196.73° C
Type I error in the context
Type I error is when the engineer's test shows that the interior of the Konodo spacecraft is below 200° C when the interior is actually above 200° C
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Over three days, Molly earns $2,568 for a local charity. On the first day, she earns twice as much as she earns on the second day. On the third day, she earns three times as much as the second day. How much does she earn on the first day?
If on the third day, she earns three times as much as the second day. The amount that she earn on the first day is $856.
How to find the amount earned?Let a = Amount earned on the first day
Let b = Amount earned on the second day
Let c = amount earned on the third day
Let a + b + c =2568,
Hence,
2b + b +3b =2568
6b =2568
b =2568/6
b =428 second day
So,
a = 2b
a =2(428)
a =856 first day
Thus
c = 3b where b = 428
c=3(428)
c=1284 third day
Check:
a +b + c = $2568
856 + 428 + 1284 = $2568
Therefore she earned $856 on the first day.
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The screenshot included A crate of medicine with a density of 2050 kilograms per cubic meter that will be shipped from England to the U.S. What is the crate's density in pounds per cubic foot?
The crate's density in pounds per cubic foot?
What is the crate's density in pounds per cubic foot?Since the crate of medicine with a density of 2050 kilograms per cubic meter will be shipped from England to the U.S, we require its density in pounds per cubic foot.
To do this, we convert the density in kilograms per cubic foot to pounds per cubic foot by using the ratios of conversion given
Since the density of the crate in kilograms per cubic meter is
2050 kg/m³, using the conversion ratios, we have
2050 kg/m³ = 2050 kg/m³ × 1 m³/35.3 ft³ × 2.2 lb/kg
= 4510 lb/m³ × 1 m³/35.3 ft³
= 127.76 lb/ft³
So, crate's density is 127.76 lb/ft³
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A survey asked 300 students to choose their favorite type of movie.
The results are shown in the following table.
(a) Find the percentage for each type of movie.
Type of movie
Action
Comedy
Drama
Thriller
Number of
students
27
42
120
111
Percentage
1%
%
%
%
X
5
Answer:
300/100%=3%
Step-by-step explanation:
sorry, can't explain.Ihave class tomorrow
Instructions: Show that the conjecture is false by finding a counterexample. Change the value of n below in order to make it a counterexample. "Two supplementary angles are not congruent."
The counterexample for "Two supplementary angles are not congruent." is
angle 100° and angle 80° are supplementary angels
angle 90° and angle 90° are supplementary angels
The instances show supplementary angles that are not congruent
What is counter examples?A specific situation that demonstrates that a statement is untrue is referred to as a counterexample.
Counterexamples provides instances that opposes the statement
In this case the two supplementary angles 100-and-80 and 90-and-90 are not congruent and hence a counterexample to the statement
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I need asap thank you
Answer:
33 degrees
Step-by-step explanation:
The square in the corner of these two vectors signifies that this is a right angle, which will always equal 90 degrees, so if you subtract angle 2's value of 57 degrees, you will be left with angle 1 as 33 degrees.
Which points are on the axes 5 units from the origin
Answer:
E and X
Step-by-step explanation:
look for the 6 then behind it
Answer:
X and E
Step-by-step explanation:
"axes" is the plural of axis. The x-axis is the flat line marked with numbers and arrows at the ends. Its labelled x on the right side.
The y-axis is the up-and-down line marked with numbers and arrows at the ends, labelled y at the top.
The origin is where the two axes cross.
Points J, E, X and P are all on the axes. But X and E are 5 units from the origin (where the lines cross) J and P are 9 units from the origin.
2, 6 and 10 were labelled on the axes, but each tick mark is an evenly spaced amount. So the 5 was unlabelled, but it is understood to be 5. See image.
Find the greatest common factor of the two numbers.
12,39
Answer:
3
Step-by-step explanation:
first factor out both the numbers
12:2*2*3
39:3*13
find the common ones and multiply them together
they both share only 3, so 3
Joe has eaten 3/5 of pizza. Jane has eaten 1/6 of a pizza. How many times more pizza has joe eaten than Jane?
Joe has eaten 3.6 times more pizza than Jane has eaten.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
Joe has eaten 3/5 of the pizza. Jane has eaten 1/6 of a pizza.
Divide the fraction number 3/5 by the fraction number 1/6. Then we have
⇒ (3/5) / (1/6)
Simplify the expression, then we have
⇒ (3/5) x 6
⇒ 3.6
Joe has eaten 3.6 times more pizza than Jane.
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Sarah is hiking on a trail near her home. She traveled 5 miles before stopping for a break. After the break, Sarah plans on increasing her speed to 3miles per hour. Which equation models the total distance, D, Sarah travels after hiking an additional h hours
The required expression for the Sarah's travel is y = 5 + 3h.
Given that,
Which equation models the total distance, D, Sarah travels after hiking additional h hours is to be determined.
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
Sarah is hiking on a trail near her home. She traveled 5 miles before stopping for a break. After the break, Sarah plans on increasing her speed to 3miles per hour.
Let the total distance hike by Sarah be y,
According to the question,
y = 5 + 3h
Thus, The required expression for the Sarah's travel is y = 5 + 3h.
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What is the y-intercept of a line that has a slope of 2 and ( - 2, 3 ) is a point on the line?
The y-intercept of the line will be equal to 7.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that a line that has a slope of 2 and ( - 2, 3 ). The y-intercept of the line will be calculated as,
y = mx + c
3 = (-2 x 2 ) +c
3 = -4 + c
c = 4 + 3
c = 7
Therefore, the y-intercept of the line will be equal to 7.
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The width of a rectangle measures (9.6w+4.7x) centimeters, and its length
measures (7.8w - 2.1x) centimeters. Which expression represents the perimeter,
in centimeters, of the rectangle?
Answer:
[tex]34.8w+5.2x[/tex] cm
Step-by-step explanation:
If the width of a rectangle measures [tex](9.6w+4.7x)[/tex] cm and its length measures [tex](7.8w-2.1x)[/tex] cm, then the perimeter of the rectangle is:
[tex]2(9.6w+4.7x)+2(7.8w-2.1x)[/tex]
[tex](19.2w+9.4x)+(15.6w-4.2x)[/tex]
[tex]19.2w+9.4x+15.6w-4.2x[/tex]
[tex]19.2w+15.6w+9.4x-4.2x[/tex]
[tex]34.8w+5.2x[/tex]
Sheila is making accessories for the soccer team. She uses 784.96 inches of fabric on headbands for 28 players and 4 coaches. She also uses 238.28 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
Answer: 3.28 inches
Step-by-step explanation:
Fabric used for players and coaches is 776.32 inches.
Number of players is 29 and coaches is 3
So fabric used for each player and coach for the headbands is
776.32/29+3 = 24.26 inches
So, for the players 24.26 of fabric will be used for the headbands.
Total fabric used for the wristbands is 247.66 inches
Fabric used for the wristband is
247.66/29 = 8.54 inches
So, total amount of fabric used by Shelia for the wristband and headband is 24.26 + 8.54 = 32.8 inches.
ADC ~ CDB by the AA triangle similarly theorem. what is the measure of AC? Round to nearest 10th
The measure of side AC in the triangle is 2.7 m
Calculating measures of sides in similar trianglesFrom the question, we are to determine the measure of AC
From the given information, we have that ΔADC is similar to ΔCDB
Thus,
We can write that
|DC| / |DB| = |AC| / |CB|
From the diagram,
|DC| = 5.5 m
|DB| = 6.3 m
|AC| = h
|CB| = 3.1 m
Then,
5.5 / 6.3 = h / 3.1
∴ h = (5.5 × 3.1) / 6.3
h = 17.05 / 6.3
h = 2.70635 m
h ≈ 2.7 m
Hence,
The length of AC is 2.7 m
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The laundry room at a hotel sent 160 bath
towels and 64 washcloths to the most rooms
they could so that each room received the
same number of each type of towel. How
many bath towels and how many washcloths
went to each room?
Answer:
5 bath towels
2 washcloths
Step-by-step explanation:
160 = 2⁵ × 5
64 = 2⁶
HCF= 2⁵ = 32
160 ÷ 32 = 5
64 ÷ 32 = 2
Neeeedddd Helpp Pls!!! I'll give brainliest to the person with the correct answer!
Show work please.
M∠M = 6x – 6 and m∠P = 4x + 10, what is m∠M?
3 times 4 times 4 times 3 times 3 times 4 = 3 (to the power of x) times 4 (to the power of y)
The value of 3 times 4 times 4 times 3 times 3 times 4 in exponent is 3³ × 4³
What is an exponent?An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
In this case, the expression given is 3 times 4 times 4 times 3 times 3 times 4. It should be noted that the 4 occurs three times as well as the 3.
Therefore, this will be 3³ × 4³.
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A trail mix is made by adding cashews that sell for $2.75 per pound to chocolate candies that sell for $1 per pound. How many of each should be used to get 50 pounds of trail mix that sells for $2 per pound?
Complete the statements.
The 50 pounds of trail mix includes [DROP DOWN 1] pounds of cashews and [DROP DOWN 2] pounds of chocolate candies.
The 50 pounds of trail mix includes 28.57 pounds of cashews and 21.43 pounds of chocolate candies.
What pounds of cashew and chocolate candies should be mixed to make the trail mix?let
x = pounds of cashewy = pounds of chocolate candiesx + y = 50
2.75x + y = 50 × 2
Solve the equation simultaneously
x + y = 50
2.75x + y = 100
Substract the equations2.75x - x = 100 - 50
1.75x = 50
x = 50/1.75
x = 28.57 pounds
Substitute into
x + y = 50
28.57 + y = 50
y = 50 + 28.57
y = 21.43 pounds
So therefore, the pounds of cashew and chocolate candies needed are 28.75 and 21.43 respectively.
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math what does g =.................
The value of g after solving the expression, 5/2-2g = 5g/2-3+g, is 1.
According to the question,
We have the following expression:
5/2-2g = 5g/2-3+g
Now, moving the terms with the same variables on one side and the integers on another side.
Note that when we move any number of term from one side to another which is in addition or subtraction will result in change of the sign from minus to plus and plus to minus.
5/2+3 = 2g+5g/2+g
Taking 2 as the least common factor on the left hand side and right hand side:
(5+6)/2 = (4g+2g+5g)/2
11/2 = 11g/2
Now, 11/2 on the left hand side can be divided by 11/2 on the right hand side:
g = 1
Hence, the value of g is 1.
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expand and simplify 3(2x+1)+(x+4)
janet and andy bowled three games. Janets scores were 119, 96, and 145. Andys scores were 127, 74, and 88. How much greater was janets total score for the three games that andys total score
Answer:
64
Step-by-step explanation:
119+89+145=353-289=127+74+88
^
64