Martin deposits $200 in a savings account that earns 5% annual interest. four years later, cary deposits $200 in an account earning the same interest. let m represent the balance in martin’s account and let c represent the amount of money in cary’s account. choose the pair of expressions that describe the accounts y years after martin opened his account. martin: 200(1.05)y cary: 200(1.05)y+4 martin: 200(1.05)y+4 cary: 200(1.05)y–4 martin: 200(0.05)y cary: 200(0.05)y–4 martin: 200(1.05)y cary: 200(1.05)y–4
Answer:
d then d again
Step-by-step explanation:
What positive number is twice it's own square
Answer: The positive number is [tex]\dfrac{1}{2}.[/tex]
Step-by-step explanation: We are given to find the positive number that is twice it's own square.
Let x denotes the required number.
Then, according to the given information, we have
[tex]x=2x^2\\\\\Rightarrow 2x^2-x=0\\\\\Rightarrow x(2x-1)=0\\\\\Rightarrow x=0,~~2x-1=0\\\\\Rightarrow x=0,~\dfrac{1}{2}.[/tex]
Sine 0 is not considered as a positive number, so the required positive number is [tex]\dfrac{1}{2}.[/tex]
Thus, the positive number is [tex]\dfrac{1}{2}.[/tex]
GUYS HELP PLEASE URGENT!!!!!!
A newborn baby weighs 3.136x10^3 units. Which unit of measure was used? grams ounces pounds tons
its grams because it cant be pounds because a baby isnt 3000 pounds, thats is just crazy!
The unit 'gram' will used to measure the weight of newborn baby in this case.
Unit conversion:
Conversion of units is the conversion between different units of measurements for the same quantity.
1 pound = 0.454kilogram1 kg = 1000 g1 ton = 1000 kg1 ounce = 0.0283 kgAccording to the given question we have,
Weight of the new born baby = [tex]3.136[/tex] × [tex]10^{3}[/tex] = 3136
From the unit conversion,
3136 pound = 1,423.744kg
3136 gram = 3136/1000 = 3.136gram
3136 ton = 3136000 kg
3136 ounce =88.7488 kg
The range of weight of new born baby in kg is 3 to 4.
Hence, only 3136 gram is possible .So, the unit 'gram' will used to measure the weight of newborn baby in this case.
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Enrique weighs 5 pounds more than twice Brendan's weight. If their total weight is 225 pounds, how much does Enrique weigh?
To find Enrique's weight, set up a system of equations based on the given information and solve for the weights of both Brendan and Enrique.
Enrique weighs 5 pounds more than twice Brendan's weight.
If their total weight is 225 pounds, you can set up a system of equations.
Let x be Brendan's weight, so Enrique's weight is 2x + 5.
From the given information, x + (2x + 5) = 225.
Solving the equation, x = 70 and Enrique's weight is 2(70) + 5 = 145 pounds.
Two trains leave stations 306 miles apart at the same time and travel toward each other. one train travels at 75 miles per hour while the other travels at 95 miles per hour. how long will it take for the two trains to meet?
Answer: It will take 1.8 hours for the two trains to meet.
Step-by-step explanation:
Since we have given that
Speed of one train = 75 mph
Speed of other train = 95 mph
Since they travel towards each other.
so, Relative speed = 75+95 = 170 mph
Distance between them = 306 miles
We need to find the time taken:
So, it becomes,
[tex]time=\dfrac{Distance}{Speed}\\\\Time=\dfrac{306}{170}\\\\Time=1.8\ hours[/tex]
Hence, it will take 1.8 hours for the two trains to meet.
Use the form of the definition of the integral given in theorem 4 to evaluate the integral x^3-3x^2
Using Newton’s cooling model, what will the temperature of a cup of hot tea be 2 hours after it is poured if its initial temperature is 200°F, the surrounding temperature is 70°F, and the value for k is 0.6?
A.130
B.109.16
C.109.76
D.71.35
E.60
What is the process that you need to follow in order to prove a circle?
Lena will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $50 and costs an additional $0.50 per mile driven. The second plan has no initial fee but costs $0.70 per mile driven. For what amount of driving do the two plans cost the same? What is the cost when the two plans cost the same
The two plans cost the same when Lena drives 250 miles, resulting in a cost of $175 for both plans, as per the given linear equation.
A linear equation is a mathematical expression that represents a straight line relationship between variables, typically in the form of ax + b = 0.
The two plans cost the same when the amount of driving satisfies the equation:
50 + 0.50x = 0.70x
Where:
50 represents the initial fee for the first plan,
0.50x represents the cost per mile for the first plan, and
0.70x represents the cost per mile for the second plan.
Now, let's solve for x:
50 + 0.50x = 0.70x
Subtract 0.50x from both sides:
50 = 0.20x
Now, divide both sides by 0.20:
x = 50 / 0.20
x = 250
So, the two plans cost the same when Lena drives 250 miles. To find the cost at this point, plug x = 250 into either plan:
For the first plan:
Cost = 50 (initial fee) + 0.50 (cost per mile) * 250
Cost = $50 + $125
Cost = $175
For the second plan:
Cost = 0.70 (cost per mile) * 250
Cost = $0.70 * $250
Cost = $175
So, when Lena drives 250 miles, both plans cost $175.
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If MNO ~XYZ,then what corresponding parts are congruent
Final answer:
In similar triangles MNO and XYZ, corresponding angles are congruent (M with X, N with Y, O with Z) and corresponding sides are in proportion (MN to XY, NO to YZ, MO to XZ).
Explanation:
If triangles MNO and XYZ are similar (denoted as MNO ~ XYZ), then their corresponding parts are congruent. Corresponding parts include angles and sides that match between the two triangles due to their similarity in shape and proportion. In similar triangles, corresponding angles are congruent, while corresponding sides are in proportion.
The corresponding congruent angles would be angle M and angle X, angle N and angle Y, and angle O and angle Z. For the sides, the lengths are proportional, which means that the ratio of MN to XY is the same as the ratio of NO to YZ, which is also the same as the ratio of MO to XZ.
Final answer:
In similar triangles MNO and XYZ, the corresponding congruent parts are angles M, N, O congruent to angles X, Y, Z respectively and sides MN, NO, OM proportional to sides XY, YZ, ZX respectively.
Explanation:
If triangles MNO and XYZ are similar (denoted as MNO ~ XYZ), it indicates that they have the same shape but not necessarily the same size. This means that their corresponding angles are congruent, and their corresponding sides are in proportion.
The corresponding congruent parts would be:
Angle M is congruent to Angle X
Angle N is congruent to Angle Y
Angle O is congruent to Angle Z
Side MN is proportional to Side XY
Side NO is proportional to Side YZSide OM is proportional to Side ZXRemember, while the angles are congruent, the sides are proportional, which means the length of the sides of one triangle is some multiple or fraction of the lengths of the corresponding sides of the other triangle.
A mother gives birth to a 9 pound baby. every 4 months, the baby gained 2 pounds. if x is the age of the baby in months, then y is the weight of the baby in pounds. find an equation of a line in the form y = mx + b that describes the baby's weight.
Final answer:
The equation of the line that represents the baby's weight as it grows is y = 0.5x + 9, where x is the age of the baby in months, and y is the weight of the baby in pounds.
Explanation:
The student is looking for an equation of a line that represents the weight of a baby as it grows. This situation can be described using a linear equation in the form of y = mx + b, where y represents the weight of the baby in pounds, x represents the age of the baby in months, m is the rate at which the baby gains weight, and b is the initial weight of the baby at birth.
Given that the baby weighs 9 pounds at birth, we have our b value as 9. It is also given that the baby gains 2 pounds every 4 months, which can be converted to a monthly weight gain of ½ pound per month (since 2 pounds ÷ 4 months = ½ pound per month). Consequently, the value of m is ½ or 0.5.
Using these values, the equation of the line that describes the baby's weight over time can be written as:
y = 0.5x + 9
This equation indicates that the baby's weight (y) is 9 pounds at birth (when x = 0) and increases by 0.5 pounds each month.
What is the difference of 28y - 16y
Jessica purchased items worth $41.23 at the local
grocery store. The cashier made a mistake while
ringing up her items, and Jessica ended up paying
$50.23. How many extra dollars did she pay?
A party was organised for thirty people at which they could have either a hamburger or a pizza. if there were five times as many hamburgers as pizzas, calculate the number of each\
There are 5 pizza and 25 hamburgers.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A party was organized for thirty people.
And, There were five times as many hamburgers as pizzas.
Now,
Let number of pizza = x
Then, Number of hamburgers = 5x
So, We get;
⇒ x + 5x = 30
⇒ 6x = 30
⇒ x = 5
Thus, Number of pizza = x
= 5
Then, Number of hamburgers = 5x
= 5 × 5 = 25
Therefore, There are 5 pizza and 25 hamburgers.
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Use the given information below, find the p-value
a., test statistic z = -1.52
The p value can simply be located given the value of the z statistic by using a standard normal probabilities distribution table.
We are given that the z value of z = - 1.52. Since z is negative this means that we are to look for the proportion or p value located to the left of z. Based on the standard normal probabilities distribution table, this is equivalent to a p value of:
p value = 0.0643
This given p value indicates that 0.0643 or 6.43% of the population is located to the left of z.
Answer:
p value = 0.0643
HELP!! QAQ
Create your own piecewise function with at least two functions. Explain, using complete sentences, the steps for graphing the function. Graph the function by hand or using a graphing software of your choice (remember to submit the graph).
An visual of the function would be really appreciated. Thanks!
What is the complete factorization of the polynomial below?
x3 - 3x2 + x - 3
Final answer:
The complete factorization of the polynomial x³ - 3x² + x - 3 is (x - 3)(x² + 3)(x + 1).
Explanation:
The complete factorization of the polynomial x³ - 3x² + x - 3 can be found by using the Rational Root Theorem and synthetic division. By trying out the possible rational roots using the Rational Root Theorem, we find that one of the roots is 3. So, we divide the polynomial by (x - 3) to get the quadratic factor and the remaining linear factor.
(x - 3) is a factor, so we divide x³ - 3x² + x - 3 by (x - 3) using synthetic division:
3|1-31-3|3030|1010
The result is x² + 3.
The remaining linear factor is 1x + 1 = x + 1.
Therefore, the complete factorization of the polynomial x³ - 3x² + x - 3 is (x - 3)(x² + 3)(x + 1).
What is the measure of the hypotenuse of an isosceles right triangle with leg lengths 6?
what is the final step to solving the inequality -2(5-4x)<6x-4
Answer:
x< 3
Step-by-step explanation:
-2(5-4x)<6x-4
multiply -2 inside the parenthesis
-2 * 5 = -10
-2 * -4x= 8x
-2(5-4x)<6x-4
-10 + 8x < 6x -4
To solve for x we need 'x' on the left hand side
Subtract 6x from both sides
-10 + 8x -6x< 6x -6x -4
-10 +2x < -4
Add 10 on both sides
-10 +10 +2x < -4+10
2x < 6
divide by 2 on both sides
x< 3
A forensic detective is called to the scene of a murder at 2 am. When she checks the temperature of the body, she sees that it is 80 degrees Fahrenheit. The temperature of the room in which the body is found is 65 degrees. If the detective uses Newton's law of cooling, what will she say is the time of death? T(t)=Ta+(To-Ta)e^(-0.1947t).
Thank you to anyone who helps! :)
Which classifications apply to the polygon? Check all that apply.
convex
concave
regular
hexagon
octagon
Answer: Concave and Hexagon.
Step-by-step explanation: In the given figure we have one angle is greater than 180 degrees.
A polygon has an angle between 180 to 360 is called a concave polygon.
Therefor given polygon is a concave polygon.
Also the given polygon has six sides.
A polygon with six sides is a hexagon.
Therefore, correct options are Concave and Hexagon.The classifications that apply to the polygon are concave and hexagon.
What is a polygon?
A polygon is a shape with at least three straight sides and angles. A regular polygon has at sides and angles of the same length and size. A convex polygon is a shape in which all of its vertices point in the outward direction. A concave polygon is a shape in which all of its vertices point in the outward direction. A hexagon is a polygon with eight sides.
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A sphere fits snugly inside a 6-in. cube as shown. what is the volume of the region inside the cube but outside the sphere
The volume of the region inside the cube but outside the sphere is approximately 187.73 in^3.
Explanation:The volume of the region inside the cube but outside the sphere can be calculated by subtracting the volume of the sphere from the volume of the cube.
Volume of the cube = side^3 = 6^3 = 216 in^3
Volume of the sphere = (4/3)πr^3
Since the sphere fits snugly inside the cube, the radius of the sphere is half the length of the side of the cube. So, r = 3/2 in.
Therefore, volume of the region = volume of the cube - volume of the sphere = 216 in^3 - (4/3)π(3/2)^3 in^3 = 216 in^3 - 9π in^3 = 216 in^3 - 28.27 in^3 ≈ 187.73 in^3.
HELP Please THANKS (:
If f(x)=square root of x+12 and g(x)=2square root of x, what is the value of (f – g)(144)? –84
–60
0
48
A regular pyramid has a height of 12 cm in a square base if the volume of the pier mid is 236 cm³ how many centimeters are in the length of one side of its base?
Find the zeros of the function.
f(x) = 9x3 - 72x2 + 135x
Joel and Melinda provide the following proofs for vertical angles to be equal:
Joel's proof: angle 2 + angle 3=180° (t is a straight line)
angle 1 + angle 2 = 180° (PQ is a straight line)
Therefore, angle 1 + angle 2 = angle 2 + angle 3 (Transitive Property of Equality)
Hence, angle 1 = angle 3 (Subtraction Property of Equality)
Melinda's proof: angle 1 + angle 2 + angle 3 + angle 4 = 360°
Therefore, angle 1 + angle 4 = 180° (t is a straight line)
Hence, angle 4 = angle 2 (Transitive Property of Equality)
Which statement is correct?
A Joels is correct
B Melindas is correct
C Both Melinda and joels is correct
D Neither is correct
The answer is A! I just did it and gotit right
If angle A measures 57 degrees and angle C is adjacent to angle A, what is the measure of angle C if the two angles are complementary?
Luisa knit a rectangular scarf that measures 4 feet by 1 foot. She wants to use the remaining 6 square feet of fabric to create a border around the scarf.
Which equation can she use to find the required width of the border x?
To solve this problem, let us recall that the formula for Area of a rectangle is:
A = l * w
Where,
l = length of one side = 4 ft
w = width of one side = 1 ft
Therefore the original area is:
Ao = 4 ft * 1 ft
Ao = 4 ft^2
Since each border would be increased by x, therefore the new l and w would be:
l = 4 + 2x
w = 1 + 2x
The new area becomes:
A = (4 + 2x) (1 + 2x)
The difference of the two would be the area of the remaining scarf:
A – Ao = 6 square ft
(4 + 2x) (1 + 2x) – 4 = 6 ---> 1
(4 + 2x) (1 + 2x) = 10 ---> 2
The equation to use can be equation 1 or equation 2.
When critiquing an observational study, which four factors should be analyzed?
A Methodology, Results, Discussion, Conclusion
B Introduction, Results, Discussion, Conclusion
C Introduction, Methodology, Results, Discussion
D Methodology, Causes, Results, Discussion
Answer:
Introduction, Methodology, Results, Discussion.
Step-by-step explanation:
yes