Answer:
8 ounces.
Step-by-step explanation:
[tex]16.85-8=8.85[/tex]
It cannot be 4 or 6 ounces as it is not likely that much water would have been wasted. It cannot be 10 ounces, as definitely more than that has been already drank. So it must be 8 ounces.
Answer:
8
Step-by-step explanation:
Suppose you park your car at a trailhead in a national park and begin a 2-hr hike to a lake at 7 A.M. on a Friday morning. On Sunday morning, you leave the lake at 7A.M. and start the 2-hr hike back to your car. Assume the lake is 3 mi from your car. Let f(t) be your distance from the car r hours after 7 A.M. on Friday morning and let g(t) be your distance from the car t hours after 7 A.M. on Sunday morning.
a. Evaluate f(0), f(2), g(0), and g(2).
b. Let h(t) = f(t) - g(t). Find h(0) and h(2).
c. Use the Intermediate Value Theorem to show that there is some point along the trail that you will pass at exactly the same time of morning on both days.
Answer:
The answer is given below
Step-by-step explanation:
The distance from the lake to the car is 3 miles and it takes 2 hours. The velocity of the hiker is 3/2 mi/hr. Therefore f(t) which is the distance from the car t hours after 7 A.M is given by:
[tex]f(t)=\frac{3}{2}t[/tex]
When coming back on Sunday morning, the distance g(t) from the car at any point in time is given by:
[tex]g(t)=3-\frac{3}{2}t[/tex]
a)
[tex]f(t)=\frac{3}{2}t\\f(0)=\frac{3}{2}(0)=0\ mile\\f(2)=\frac{3}{2}(2)=3\ miles[/tex]
[tex]g(t)=3-\frac{3}{2}t\\g(0)=3-\frac{3}{2}(0)=3\ miles\\g(2)=3-\frac{3}{2}(2)=2-2=0\ mile\\[/tex]
b)
[tex]h(t)=f(t)-g(t)=\frac{3}{2}t -(3-\frac{3}{2}t)=\frac{3}{2}t -3+\frac{3}{2}t=3t-3\\h(t)=3t-3\\h(0)=3(0)-3=0-3=-3\\h(2)=3(2)-3=6-3=3[/tex]
c)
According to Intermediate Value Theorem, there exist a point b where f(b) = g(b). i.e. f(b) - g(b) = 0
[tex]h(b)=f(b)-g(b)=0\\h(0)=-3,h(2)=3[/tex]
This means there exist a point b within the interval [-3, 3] where f(b) - g(b) = 0
You invest $2500 in an account to save for college. Account 1 pays 6% annual interest compounded quarterly. Account 2 pays 4% annual interest compounded continuously. Which account should you choose to obtain the greater amount in 10 years and why.
Thank you!!
Answer: Account 2
Step-by-step explanation:
Account 1)
Formula for CI
Amount = p(1 + r/n)^nt
A = 2500 (1 + .06/4)^4x10
A = 2500 (1 + 0.015)^40
A = 2500 (1.015)^40
A = 4535.05
Account 2.
Formula for CI for interest compounded continously
A = Pe^rt
A = 2500 x e^0.06 x 10
A = 2500 x e^0.6
A = 2500e^3/5
A = 4555.297
Account 2 should you choose to obtain the greater amount in 10 years.
Important information:You invest $2500 in an account to save for college. Account 1 pays 6% annual interest compounded quarterly. Account 2 pays 4% annual interest compounded continuously.
Calculation of the amount in both the accounts:For Account 1
[tex]Amount = p(1 + r\div n)^{nt}\\\\A = 2500 (1 + .06\div 4)^4\times 10\\\\A = 2500 (1 + 0.015)^{40}\\\\A = 2500 (1.015)^{40}[/tex]
A = 4535.05
For Account 2:
A = Pe^rt
[tex]A = 2500 \times e^0.06 \times 10\\\\A = 2500 \times e^0.6\\\\A = 2500e^3/5[/tex]
A = 4555.297
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59.6487 to 2 decimal places
Answer:
59.65
Step-by-step explanation:
2 decimal places is to the hundredths place.
Answer: 59.65
Step-by-step explanation: When rounding a number to a given place, look at the next place y o the right. If that digit is 5 or more, "round up" by adding one to the given place.
If the number to the right is 4 or less, leave the given place "as is"
In this example, the hundredths place is 4, the place to the right has an 8. So you round up the 4 to a 5. You end up with 59.65
From a group of 8 women and 6 men, a committee consisting of 3 men and 3 womenis to be formed. How many different committees are possible if 2 of the men refuse toserve together? How many different committees are possible if 1 man and 1 womanrefuse to serve together?
Answer:
a) 896 ways
c) 910 ways
Step-by-step explanation:
The question is a combination problem since it has to do with selection. In combination, if r object is selected from a pool of n objects, this can be done in nCr ways.
nCr = n!/(n-r)!r!
If from a group of 8 women and 6 men, a committee consisting of 3 men and 3 women is to be formed, we need to first calculate the total committee formed without any condition.
8C3 × 6C3
= 8!/5!3! × 6!/3!3!
= 8×7×6×5!/5!×6 × 6×5×4×3!/3!×6
= 56×20
= 1120ways
Now if;
a) two of the men refuse to serve together.
Since two men refuse to serve together, we will select 1 man from remaining 4 men since two has already been selected then select 3 from 8 women as shown.
4C1×8C3
= 4×56
= 224ways
Number of ways this can be done will be 1120-224 = 896ways
b) 1 man and 1 woman refuse to serve together
We need to choose 2 men from remaining 5 and 2 women from the rest of the men which is 7 as shown:
= (8-1)C(3-1) × (6-1)C(3-1)
= 7C2 × 5C2
= 7!/5!2! × 5!/3!2!
= 7×6×5!/5!×2 × 5×4×3!/3!×2
= 21×10
= 210ways
The number of ways this can be done will be 1120-210 = 910ways
7.5. 15. 30. None of the choices are correct.
Answer:
15
Step-by-step explanation:
Since we are given 2 sets of angles, we can determine the 2 triangles as congruent using AA Congruence Theorem. So if mAB = 15, then mCB also equals 15.
Step-by-step explanation:
∠ABC forms and Obtuse angle ( A measure greater than 90° but less than 180°)
mAB is 90° and mCB is 30°
If AB = 15, then CB must be 12.
[tex]\frac{180}{15} = 12[/tex]
Please help me! Thx if you do
Answer:
3
Step-by-step explanation:
6(2x-3)=-(x-9)+4x (Distributive property)
12x-18=-x+9+4x
12x-4x+x=9+18 (Collecting like terms)
9x=27 (Division)
x=3
Hope I am correct :)
Answer:
3Option D is the correct option.
Step-by-step explanation:
6 ( 2x - 3 ) = - ( X - 9 ) + 4x
Distribute 6 through the parantheses
12x - 18 = - ( X - 9) + 4x
When there is a (-) in front of an expression in parantheses, change the sign of each term in the expression
12x - 18 = -x + 9 + 4x
Collect like terms
12x - 18 = 3x + 9
Move variable to Left hand side and change its sign
12x - 3x - 18 = 9
Move constant to Right hand side and change its sign
12x - 3x = 9 + 18
collect like term
9x = 9 + 18
Add the numbers
9x = 27
Divide both sides of the equation by 9
9x /9 = 27/ 9
Calculate
X = 3
Hope this helps....
Good luck on your assignment...
Help! Which choice is the most efficient first step to solve this set of equations?
Answer:
Substitute 3x - 5 for y in the second equation.
Step-by-step explanation:
Generally, to solve the system of linear equations of x and y, the first step would be trying to eliminate x (or y).
Then turn the system into the equation of only y (or x).
Next, try to solve for y (or x).
Then substitute the solved y (or x) into the original system to work out x (or y).
**********
3 options (1 addition, 2 subtractions) do not eliminate x or y (x and y still exist after manipulation).
=> Remaining option relating substitution would be a reasonable choice.
Please answer this in two minutes
x = 144 degrees
We know there are 10 sides on this polygon, and we know the sum of interior angles in a regular polygon is represented as 180*(s-2) where s is the number of sides.
With this, we know that the sum of interior angles on a 10-sided regular polygon is 180*(10-2)=1440.
We also know that the measure of angle x = the measure of any other interior angle in the 10-sided polygon.
Using substitution, we know that 10x = 1440 degrees so x = 144 degrees.
The value of x for the 10-sided polygon is x = 144 degrees.
What is a polygon?A polygon is a two-dimensional, closed shape that is flat or plane and is bounded by straight sides. Its sides are not curved. A polygon's edges are another name for its sides. The vertices (or corners) of a polygon are the places where two sides converge.
We know there are 10 sides on this polygon, and we know the sum of interior angles in a regular polygon is represented as 180*(s-2) where s is the number of sides.
With this, we know that the sum of interior angles on a 10-sided regular polygon is 180 x (10-2)=1440.
We also know that the measure of angle x = the measure of any other interior angle in the 10-sided polygon.
Using substitution, we know that 10x = 1440 degrees so x = 144 degrees.
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Graphing Exponential Functions: Which function is graphed below?
A) y=1/3(3)^x
B) y=3(1/3)^x
C) y=)1/2)^+2
D) y=(2)^x-1
Thank you!!
Answer:
B
Step-by-step explanation:
The y-intercept (or initial value) is 3 which means the coefficient of the exponential term is 3. The only answer choice that follows this is choice B.
tim spends 25% of his time at the gym dooing leg exercises , 1/5 on shoulder exercises , 0.35 on biceps exercises , and warming up . what percentage of time does tim spend warming up
Answer:
20%
Step-by-step explanation:
25%+(35%)+(20%)=80%
100-80=20%
The number of text messages that Reza sent each day so far in this billing cycle is shown on the dot plot. A number line going from 1 to 13. 2 dots are above 2. 1 dot is above 3. 3 dots are above 6. 2 dots are above 7. 3 dots are above 8. 1 dot is above 11. 2 dots are above 12. Which statement must be true according to the dot plot? The data is symmetric and shows that he typically sent about 6 to 8 text messages per day. The data is symmetric and shows that he sent 11 or 12 texts with the same frequency that he sent 1 or 2 texts. The data is skewed and shows that he typically sent about 6 to 8 text messages per day. The data is skewed and shows that he sent 11 or 12 texts with the same frequency that he sent 1 or 2 texts.
Complete Question:
The number of text messages that Reza sent each day so far in this billing cycle is shown on the dot plot.
Which statement must be true according to the dot plot?
A) The data is symmetric and shows that he typically sent about 6 to 8 text messages per day.
B) The data is symmetric and shows that he sent 11 or 12 texts with the same frequency that he sent 1 or 2 texts.
C) The data is skewed and shows that he typically sent about 6 to 8 text messages per day.
D) The data is skewed and shows that he sent 11 or 12 texts with the same frequency that he sent 1 or 2 texts
*Check attachment for the dot plot referred to
Answer:
A. The data is symmetric and shows that he typically sent about 6 to 8 text messages per day
Step-by-step explanation:
Taking a look at the dot plot given in the attachment below, we can observe that most of the data set are concentrated in the middle of the dot plot than both ends of the dot plot. With this, we can infer that the distribution of the data is symmetric.
The dot plot also tells us that, 6 and 8 text messages have more frequency than any other data set on the dot plot. This also suggests that Reza usually sends 6 to 8 messages in a day.
Therefore, the statement that is true about the dot plot is:
"A. The data is symmetric and shows that he typically sent about 6 to 8 text messages per day"
Answer:
A
Step-by-step explanation:
PLEASE HELP FAST
answers:
a.) 4
b.) 10
c.) 6
d.) 1
Answer:
4
Step-by-step explanation:
There are 5 points. So there are 4 segments. The segments are the line between two points.
Assume that all triangles have interior angles less than 90°.A farmer has a triangular field with sides that measure 40 metres (side AB), 35 metres (side BC), and 38 metres (side CA). What are the measures of the angles A, B, and C in this field?
Answer:
djal3924+3820&282039392#283830818385
A cylindrical cardboard tube with a diameter of 8 centimeters and a height of 20 centimeters is used to package a gift. A cylinder has a height of 20 centimeters and a diameter of 8 centimeters. What is the approximate volume of the tube? Round to the nearest whole cubic centimeter. 1,005 cm3 1,340 cm3 3,351 cm3 4,021 cm3
Answer:
4021 cm^3
Step-by-step explanation:
The volume of a cylinder can be found using the following formula.
[tex]V=\pi r^2h[/tex]
where r is the radius and h is the height.
We know the cylinder has a height of 20 centimeters and a diameter of 8 centimeters.
h= 20 cm
d= 8 cm
Substitute these values into the formula.
[tex]V=\pi (8 cm^2) * 20 cm[/tex]
First, evaluate the exponent.
8 cm^2= 8 cm * 8 cm= 64 cm
[tex]V=\pi * 64 cm^2*20 cm[/tex]
Multiply 64 cm^2 and 20 cm
[tex]V=\pi *1280 cm^3[/tex]
Multiply 1280 cm^3 and pi
[tex]V=4021.2386 cm^3[/tex]
Round to the nearest cubic centimeter. The 2 in the tenth place tells us to leave the number as is.
[tex]V= 4,021 cm^3[/tex]
The volume is about 4,021 centimeters^3.
The approximate volume of the tube is 1005 cm³.
What is a cylinder?A cylinder is a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base.
Given that a cardboard cylinder has a diameter of 8 centimeters and a height of 20 centimeters, we need to find the volume of the cylinder,
The volume of the cylinder = π × radius² × height
Radius = diameter / 2 = 8/2 = 4 cm
Therefore,
Volume = π × radius² × height
= 3.14 × 4² × 20
= 3.14 × 16 × 20
= 1004.8 ≈ 1005
Hence, the approximate volume of the tube is 1005 cm³.
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Wooden houses are being built on a concrete base.Each base needs 400 kg of concrete. A cement truck carries 9 tonnes of concrete. How many bases can be laid from one truck load of concrete?
Answer: 22.5
Step-by-step explanation:
From the question, we are informed that wooden houses are being built on a concrete base and that each base needs 400 kg of concrete. We are further told that cement truck carries 9 tonnes of concrete.
To calculate the amount of bases that can be laid from one truck load of concrete, we first have to convert the 9 tonnes of concrete to kilogram. It should be noted that:
1000kg = 1 ton
9 tonnes = 9 × 1000 = 9000kg
Since each base needs 400 kg of concrete, the number of bases can be laid from one truck load of concrete will then be:
= 9000kg/400kg
= 22.5 bases
The box plots represent the birth weights, in pounds, of babies born full term at a hospital during one week.
Answer:
Hiya, Need more explanation, and since you seem to be talking of a graph, maybe provide a picture of the graph
Thanks
Given the proportion 3/4 = x/10 , the value of x is:
Answer:
7.5
Step-by-step explanation:
given:
3/4 = x/10 (multiply both sides by 10)
(3/4)(10) = x
x = 30/4
x = 7.5
The value of x is 7.5
Given:
The proportion 3/4 = x/10
3/4 = x/10
30 = 4x
30/4 = x
7.5 = x
Therefore, the final answer is 7.5.
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factor by using the difference of two cubes
(2x)³- 8
Answer:
[tex](2x + 2)( {4x}^{2} - 4x + 4)[/tex]Solution,
[tex] {(2x)}^{3} - 8 \\ [/tex]
[tex]( {2x)}^{3} - {(2)}^{3} [/tex]
Use the formula:
[tex] {a}^{3} - {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} )[/tex]
now,
[tex](2x + 2)( {(2x)}^{2} - 2x \times 2 + {(2)}^{2} )[/tex]
[tex](2x + 2)( {4x}^{2} - 4x + 4)[/tex]
Hope this helps...
Good luck on your assignment...
Find the x- and y-intercept of the line.
5x – 4y = 40
A x-intercept is -4; y-intercept is 5.
B x-intercept is - 10; y-intercept is 8.
Cx-intercept is 5; y-intercept is -4.
D x-intercept is 8; y-intercept is -10.
Answer:
D
Step-by-step explanation:
you can put the function in your graphing calculator & the x-intercept is where the line crosses threw the line that goes left & right vise versa for the y-intercept.
6. Yolanda's Purse
Yolanda finally cleaned her purse, and she found 40 coins at the bottom of her purse! All her
coins were dimes and pennies. Altogether she had $2.29. How many dimes and pennies did
she find? Make your own chart.
Answer:
She found 19 pennies and 21 dimes
Step-by-step explanation:
Let the number of dimes present be d and the number of pennies present be p
From the question, the total of both is 40
Mathematically;
p + d = 40 •••••••(i)
While a penny worths 1 cent, a dime is worth 10 cents
Total penny amount would be 1 * p = p cents
While total dime amount would be 10 * d = 10d cents
Before we add both to give the total amount, let’s convert this total amount to cents and that would be 2.29 * 100 = 229 cents
So mathematically;
p + 10d = 229 •••••••(ii)
So let’s solve both equations simultaneously
From i) p = 40 - d
let’s put this into equation ii
40 - d + 10d = 229
40 + 9d = 229
9d = 229-40
9d = 189
d = 189/9
d = 21
Recall;
P = 40-d
P = 40-21
P = 19
The segments shown below could form a triangle
Answer:
yes it can form an isosceles triangle. when you join these lines AC will be the base and BC andAB will be two equal sides of an isosceles triangle.
Answer:
True i think
Step-by-step explanation:
tell me if you got it right. (btw switch to chrome its faster)
Factorise 8p^2-12/5p^2+6/25p-1/125
Answer:
[tex]8p^2-\frac{12}{5}p^2+\frac{6}{25}p-\frac{1}{125}=\frac{(p+\frac{11}{140})(p+\frac{1}{125})}{125}[/tex]
Step-by-step explanation:
You have the following polynomial:
[tex]8p^2-\frac{12}{5}p^2+\frac{6}{25}p-\frac{1}{125}[/tex] (1)
In order to obtain the factors of the previous polynomial, first you can multiply the polynomial for 125 to obtain only integer coefficients, but also you have to divide for 125, as follow:
[tex](8p^2-\frac{12}{5}p^2+\frac{6}{25}p-\frac{1}{125})\frac{125}{125}\\\\=\frac{1000p^2-300p^2+30p-1}{125}[/tex]
[tex]=\frac{700p^2+30p-1}{125}[/tex] (2)
Next, you use the quadratic formula to get the factors of the numerator of the previous expression:
[tex]p_{1,2}=\frac{-30\pm\sqrt{(30)^2-4(700)(-1)}}{2(700)}\\\\p_{1,2}=\frac{-30\pm 80}{1400}\\\\p_1=-\frac{11}{140}\\\\p_2=-\frac{1}{28}[/tex]
The factors are (p-p1) and (p-p2), then you have in the equation (2) the following factorization:
[tex]8p^2-\frac{12}{5}p^2+\frac{6}{25}p-\frac{1}{125}=\frac{(p+\frac{11}{140})(p+\frac{1}{125})}{125}[/tex]
9 + 4(x - 3) please help me!!!!!
Answer:
4x-3
Step-by-step explanation:
9+4x-12
9-12 = -3
4x-3
Answer:
4x - 3
Step-by-step explanation:
You can first take out 9 and solve for 4 (x - 3) which is 4x - 12. Now, you can put 9 back into the equation so it will be 9 + 4x - 12. We can simplify a bit further which will give us 4x - 3.
5. Three business partners Bela, Joan and Trinity contributed Ksh.112,000.Ksh.128,000 and Ksh.128,000
respectively to start a business. They agreed to share their profit as follows:
30% to be shared equally
30% to be shared in the ratio of their contributions
40% to be retained for the running of the business.
If at the end of the year the business realized a profit of ksh. 1,350,000
Calculate
(1mk)
a) The amount of money retained for the running of the business at the end of the year
40% is kept for the running of the business.
Multiply the profit by 40%
1,350,000 x 0.40 = 540,000
The amount kept for the business is 540,000
A student knows the height of a pyramid and the area of its base. What should the student do to find the volume of the pyramid
Answer:
Multiply the area of the base by the height and divide by 3.
Step-by-step explanation:
V = (1/3)Bh
where B = area of the base, and
h = height
Answer: Multiply the area of the base by the height and divide by 3.
Answer:
We khow that the volume of a pyramid is equal the product of the base and the height over 3
So he just needs to multiply them together then divide the result by 3
Find side AB and round your answer to the nearest hundredth, help please.
Answer:
? = 5.12
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin B = opp/ hyp
sin 65= 5/ ?
? = 5/ sin 65
? =5.516889595
To the nearest hundredth
? = 5.12
which are exterior angles?
Convert 25 km to feet
Answer: 82,020.997
Step-by-step explanation:
Which rules could describe the rotation? Select two options. R0, 90° R0, 180° R0, 270° (x, y) → (–y, x) (x, y) → (–x, –y)
Answer:
R0,180(x,y)->(-x,-y)
Step-by-step explanation:
R0,180(x,y)->(-x,-y)
We note that
X(-2,2) has been transformed to X'(2,-2), and
Y(1,2) has been transformed to Y'(-1.-2)
[tex]\bold{R_0,\ 180^{\circ}}\ \ and \ \ \bold{(x,y)\longrightarrow (-x,-y)}[/tex] are the choice that's description can be defined as follows:
It implies we rotate the triangle 900 times clockwise.The point Z has been on the Positive Y-Axis, rotating this Figure by 1800 will place that on the Negative Y-Axis. In addition, Point Y results in the Fourth Quadrant.We can observe that the solution figure has been flipped twice along the vertical axis and once along the horizontal plane.Both X and Y values would be multiplied by -1 if we applied this change.Therefore, the final choice are "[tex]\bold{R_0,\ 180^{\circ}}\ \ and \ \ \bold{(x,y)\longrightarrow (-x,-y)}[/tex]".
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Determine the differential equation of the family of curves x² +y² = 2cy.
Use geobra to draw the family of curves for c = -3,-2,-1,2,3
Answer:
[tex]\dfrac{dy}{dx}\left ( \dfrac{x^2+y^2}{2\times y}-y \right )=x[/tex]
Step-by-step explanation:
Given that
[tex]x^2+y^2=2cy----(1)[/tex]
Now by differentiating the above equation with respect to x
[tex]2\times x+2\times y\times \dfrac{dy}{dx}=2\times c\times \dfrac{dy}{dx}[/tex]
[tex]x+ y\times \dfrac{dy}{dx}= c\times \dfrac{dy}{dx}-----(2)[/tex]
Form the above equation (1)
[tex]c=\dfrac{x^2+y^2}{2\times y}[/tex]
Putting the value of c in the equation (2)
[tex]x+ y\times \dfrac{dy}{dx}= \dfrac{x^2+y^2}{2\times y}\times \dfrac{dy}{dx}\\\dfrac{dy}{dx}\left ( \dfrac{x^2+y^2}{2\times y}-y \right )=x[/tex]
Thus the differential equation of the given curve will be
[tex]\dfrac{dy}{dx}\left ( \dfrac{x^2+y^2}{2\times y}-y \right )=x[/tex]
Curve for different value of c :
x² +y² = 2 c y
The above equation is an equation of a circle.That circle is having center on the y-axis.