If Zach moved the existing sand from the old terrarium into the new terrarium , then the sand in the new terrarium will be 5cm deep .
The dimensions of the old terrarium is = 20 by 50 cm ;
The dimensions of the new terrarium is = 25 by 64 cm ;
So , amount of sand that Zach has is = Volume of sand in the old terrarium, that is ( Area of base of the old terrarium) × (height of sand) ;
Volume of Sand = 20 × 50 × 8 = 8000 cm³ ;
When Zach moves the sand to the new terrarium, volume of sand will be same, so we can write the equation ;
⇒ 20 × 50 × 8 = 25 × 64 × h ;
where h is = height of sand in new terrarium.
Now solving for h, we get ;
⇒ h = (20 × 50 × 8 cm)/(25 × 64 )
⇒h = 8000/1600 ;
⇒ h = 5 cm ;
Therefore, the sand will be 5 centimeters deep in the new terrarium.
Learn more about Volume here
https://brainly.com/question/29424737
#SPJ4
The given question is incomplete , the complete question is
Zach keeps his pet chameleon pinky in a terrarium with the dimensions 20 by 50 cm . there's sand in the bottom of the terrarium that reaches a height of 8 88 centimeters.
Zach gets a new terrarium for pinky that is larger. the base of the new terrarium is 25 by 64 centimeters. Zach moved the existing sand to the new terrarium. how deep will the sand be in the new terrarium ?
the tortoise and the hare are running a 1 km race. after running comfortably for 7 s, the hare is so far ahead that he decides to take a nap under a tree, 100 m away from the finish line. if the tortoise is moving constantly at a speed of 0.27 m/s, and the maximum speed of the hare is 15 m/s, how long can the hare afford to nap if he does not want to lose the race?
The hare can afford to nap for approximately 3686.33 seconds if he does not want to lose the race.
We can use the time it takes the hare to run 100 m to determine how long he can afford to nap.
First, let's find the time it takes the hare to run the 100 m:
t = d / v
Where t is the time, d is the distance, and v is the velocity (speed) of the hare.
t = 100 m / 15 m/s
t = 6.67 s
Next, let's find the time it takes the tortoise to run 1 km (1000 m):
t = d / v
Where t is the time, d is the distance, and v is the velocity (speed) of the tortoise.
t = 1000 m / 0.27 m/s
t = 3700 s
So, the time it takes the tortoise to run the race is 3700 s. The time it takes the hare to run the first 900 m is 7 s. Therefore, the time the hare has left to nap is:
3700 s - 7 s = 3693 s
And the time it takes the hare to run the last 100 m is 6.67 s. Therefore, the hare can afford to nap for:
3693 s - 6.67 s = 3686.33 s
So, the hare can afford to nap for approximately 3686.33 seconds if he does not want to lose the race.
Learn more about velocity here brainly.com/question/18084516
#SPJ4
the days to maturity for a sample of five money market funds are shown here. the dollar amounts invested in the funds are provided. days to maturitydollar value ($ millions) 1515 1110 725 515 410 use the weighted mean to determine the mean number of days to maturity for dollars invested in these five money market funds. round your answer to decimal places. days
The mean number of days to maturity for dollars invested in these five money market funds is approximately 8.95 days.
To calculate the weighted mean of the days to maturity, we need to multiply each value of days to maturity by its corresponding dollar value, sum the products, and divide the result by the total dollar value.
The calculation for the weighted mean is as follows:
Weighted Mean = (D1 x V1 + D2 x V2 + D3 x V3 + D4 x V4 + D5 x V5) / (V1 + V2 + V3 + V4 + V5)
where D represents the days to maturity and V represents the dollar value.
Using the given values, we can plug them into the formula and get:
Weighted Mean = (15 x 15 + 11 x 10 + 7 x 25 + 5 x 15 + 4 x 10) / (15 + 10 + 25 + 15 + 10)
Weighted Mean = 8.95 (rounded to two decimal places)
To learn more about mean here:
https://brainly.com/question/12789483
#SPJ4
Multiply 2 by 2 until you get 4 numbers.
I got 1024 but its not right
Answer: 1024
Step-by-step explanation:
2 x 2 is 4
4 x 2 is 8
8 x 2 is 16
16 x 2 is 32
32 x 2 is 64
64 x 2 is 128
128 x 2 is 256
256 x 2 is 512
512 x 2 is 1024
A dietician recommends 48 grams of protein each day for his patient. At the end of the day, the patient has only eaten 40 grams of protein. What percent of her daily intake has the patient eaten?
Answer:
83%
Step-by-step explanation:
To find the percentage divide 40 by 48
40/48 = 0.83333333333333
Round to 0.83
Multiply by 100
The patient has only eaten 83% of her daily intake.
a projectile travels a distance of 800 meters with an initial velocity of 200 m/s. what two firing angles could be used to launch the projectile? how long does it take each projectile to hit the ground
a. The two firing angles of the projectile are 5.65° and 174.35°
b. The time it takes the projectile to hit the ground is 4.02 s
What is a projectile?A projectile is an object that follows a parabolic path when thrown into the air.
a. How to find the two firing angles?Given that a projectile travels a distance of 800 meters with an initial velocity of 200 m/s, to find the firing angles, we use the formula for the range of a projectile.
What is the range of a projectile?The range of a projectile is its horizontal distance. It is given by R = u²sin2Ф/g where
u = initial velocity of projectile, Ф = angle of projection and g = acceleration due to gravity = 9.8 m/s²Given that we require Ф, the angle of projection. Making it subject of the formula, we have that
Ф = [sin⁻¹(gR/u²)]/2
Given that
u = 200 m/s and R = 800 mSubstituting the values of the variables into the equation, we have
Ф = [sin⁻¹(gR/u²)]/2
Ф = [sin⁻¹(9.8 m/s² × 800 m/(200 m/s)²)]/2
Ф = [sin⁻¹(9.8 m/s² × 800 m/(40000 m²/s²)]/2
Ф = [sin⁻¹(9.8 m²/s² × 1/50 m²/s²)]/2
Ф = [sin⁻¹(0.196)]/2
Ф = 11.30°/2
Ф = 5.65°
Since sin is positive in the second qudrant also, the second angle is
Ф = 180° - 5.65°
= 174.35°
So, the angle are 5.65° and 174.35°
b. How long does it take the projectile to hit thye ground?To find how long it takes the projectile to hit the ground, we use the formula for time of flight of a projectile.
T = 2usinФ/g where
u = initial velocity of projectile, Ф = angle of projection and g = acceleration due to gravitySince
u = 200 m/'sФ = 5.65° andg = 9.8 m/s²Substituting the values of the variables into the equation, we have
T = 2usinФ/g
T = 2(200 m/s)sin5.65° ÷ 9.8 m/s²
T = 400 m/s × 0.09845 ÷ 9.8 m/s²
T = 39.381 m/s ÷ 9.8 m/s²
T = 4.02 s
So, the time it takes the projectile to hit the ground is 4.02 s
Learn more about projectile here:
https://brainly.com/question/30579228
#SPJ1
PLEASE SHOW UR WORK ANSWER QUICK
The profit that they will make if they have 24 dogs for adoption is given as follows:
$160.
How to obtain the profit?The profit is obtained with the subtraction of the revenue by the costs.
The revenue and the costs for this problem are obtained as follows:
Revenue: $45 for each of the 24 dogs adopted.Costs: $920 on supplies.Hence the profit made is obtained as follows:
Profit = 45 x 24 - 920
Profit = $160.
More can be learned about profit functions at https://brainly.com/question/25638609
#SPJ1
Select the correct point
One linear equation is defined by points (1,6) and (3, 7), while the other is defined by points (3,6) and (5,8). Which point represents the solution of
this system of equations?
Answer:
Step-by-step explanation:
o find the solution of a system of linear equations, we can find the point where the two lines intersect. The point of intersection represents the solution to the system of equations.
The first linear equation can be determined by finding its slope and y-intercept using the given points:
m = (7 - 6) / (3 - 1) = 1
b = 6 - m * 1 = 6 - 1 * 1 = 5
y = mx + b
y = x + 5
The second linear equation can be found similarly:
m = (8 - 6) / (5 - 3) = 1
b = 6 - m * 3 = 6 - 1 * 3 = 3
y = mx + b
y = x + 3
Since the two lines have the same slope, they are coincident and represent the same line. The solution to the system of equations is therefore any point on this line, but since we were asked for a specific point, we can choose (3,6) as the solution.
Use the Distributive Property to solve each equation.
a. −1/2(b−6)= 5
b. 0.4(x−0.45)= 9.2
c. −4(p−212)=44
please help
The required answers are
a) b = -4
b) x = 23.45
c) p = 201
Distributive Property:The distributive property implies that multiplying a number by the sum of two or more addends yields the same result as dividing the multiplier, multiplying each addend individually, and combining the products . It can be given as,
a (b+c) = d
[tex](a*b) + (a*c) = d[/tex]
Now in the given question,
a) −1/2(b−6)= 5
by distributive property , we have
[tex](\frac{-1}{2} *b)-(\frac{-1}{2}*6 )=5\\\frac{-1}{2}b+3=5\\\frac{-1}{2}b=2\\b=-4[/tex]
b) 0.4(x−0.45)= 9.2
by distributive property , we have
0.4x - 0.4(0.45) =9.2
0.4x -0.18 = 9.2
0.4x = 9.38
x = 23.45
c) −4(p−212)=44
by distributive property , we have
-4p +4 (212) = 44
-4p + 848 =44
-4p = 44 - 848
-4p = -804
p = 201
Learn more about distributive property , visit:
https://brainly.com/question/6276874
#SPJ1
hospital records show that 12% of all patients are admitted for heart disease, 16% are admitted for cancer (oncology) treatment, and 4% receive both coronary and oncology care. what is the probability that a randomly selected patient is admitted for coronary care, oncology or both? (note that heart disease is a coronary care issue.)
The probability of randomly selected patient selected for coronary, oncology or both is equal to P( H∪C ) = 0.24.
Let patient admitted with heart disease represented by P(H)
P(H) = 12%
= 0.12
And patient admitted for cancer disease represented by P(C)
P(H) = 16%
= 0.16
Percent of patient received both coronary and oncology = 4%
P( H∩C ) = 0.04
Probability of randomly selected patient admitted for coronary, oncology or both is :
P( H∪C ) = P(H) + P(C) - P(H∩C )
⇒P( H∪C ) = 0.12 + 0.16 - 0.04
⇒ P( H∪C ) = 0.24
Therefore, the probability of randomly selected patient getting treatment for coronary, oncology or both is given by P( H∪C ) = 0.24.
Learn more about probability here
brainly.com/question/11234923
#SPJ4
2. Two observers are 600 ft apart on opposite sides of a flagpole. The angles of elevation from the
observers to the top of the pole are 19 and 21°. Find the height of the flagpole. Round to the nearest
foot.
The height of the flagpole is 110 feet.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
From the figure,
tan 19 = f/x
tan 21 = f/(600 - x)
Now,
tan 16 x = tan 21 x (600 - x)
0.34x = 0.38 x 600 - 0.38x
0.34x = 230 - 0.38x
0.34x + 0.38x = 230
0.72x = 230
x = 319
Now,
tan 19 = f/319
0.34 x 319 = f
f = 109.8
f = 110 feet
Thus,
110 feet is the height of the flagpole.
Learn more about trigonometric identities here:
https://brainly.com/question/14746686
#SPJ1
I need help with this please
Answer:
see explanation
Step-by-step explanation:
given sinΘ = - [tex]\frac{3}{5}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]
the negative sign indicates sinΘ is in the third quadrant where sinΘ < 0
this is a 3- 4- 5 right triangle with opposite = 3 and hypotenuse = 5
then the adjacent side = 4
cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = - [tex]\frac{4}{5}[/tex] ( since cosΘ < 0 in third quadrant )
secΘ = [tex]\frac{1}{cos0}[/tex] = [tex]\frac{1}{-\frac{4}{5} }[/tex] = - [tex]\frac{5}{4}[/tex]
tanΘ
= [tex]\frac{sin0}{cos0}[/tex]
= [tex]\frac{-\frac{3}{5} }{-\frac{4}{5} }[/tex]
= - [tex]\frac{3}{5}[/tex] × - [tex]\frac{5}{4}[/tex]
= [tex]\frac{3}{4}[/tex]
Simplify Fully (Negative powers)
Answer:
[tex]\frac{y^2}{4x^5}[/tex]
Step-by-step explanation:
Used Exponents Properties :
[tex]\blacksquare \left( a\times b\right)^{n} =a^{n}\times b^{n}\\\blacksquare \left( a^{n}\right)^{m} =a^{n\times m}\\\blacksquare \left( \frac{a}{b} \right)^{n} =\frac{a^{n}}{b^{n}}[/tex]
==========================
[tex]\begin{aligned}\left(\frac{256 \times x^{20}}{y^8}\right)^{-\frac{1}{4}} & =\left(\frac{y^8}{2^8 \times x^{20}}\right)^{\frac{1}{4}} \\& =\frac{\left(y^8\right)^{\frac{1}{4}}}{\left(2^8 \times x^{20}\right)^{\frac{1}{4}}} \\& =\frac{y^{8 \times \frac{1}{4}}}{\left(2^8\right)^{\frac{1}{4}} \times\left(x^{20}\right)^{\frac{1}{4}}} \\& =\frac{y^{\frac{8}{4}}}{2^{\frac{8}{4}} \times x^{\frac{20}{4}}} \\& =\frac{y^2}{2^2 x^5}\\& =\frac{y^2}{4 x^5}\end{aligned}[/tex]
what is the slope of the line that contains the points (-2,6) and (6,-3)?
PLEASE SHOW WORK
Answer: [tex]-\frac{9}{8}[/tex]
Step-by-step explanation:
If you are given two points of a line, the slope is defined as rise/run. Rise is the difference in y coordinates, (think about it, going UP is RISING), and Run is the difference in x coordinates, (again its pretty intuitive.)
So Slope = [tex]\frac{y_{2} - y_{1}}{x_{2}-x_{1}}[/tex]
This can be calculated with the coordinates of the two points, (order wont matter youll get the same answer).
Slope = (-3-6)/(6-(-2)) = -9/8
OR, (going the other way)
Slope = (6-(-3))/(-2-6) = 9/-8 = -9/8
Easy!
consider two boxes, one containing 1 black and 1 white marble, and other 2 black and 1 white marble. a box is selected at random, and a marble is drawn from it at random. what is the probability that the marble is black? what is the probability that the first box was the one selected given that the marble is white?
The probability that the first box was the one selected given that the marble is white is [tex]\frac{7}{12}[/tex] .
Probability is the likelihood that an event will occur.
The likelihood of an occurrence A provided that an earlier event B has already happened is known as conditional probability.
the two boxes are marked as B1, B2
Number of black balls: 1
Number of white balls: 1
Number of black balls in the box: 2,
Number of white balls: 1.
B and W should stand for black and white marble.
Therefore, the likelihood that either box will be selected is [tex]\frac{1}{2}[/tex]
Probability of selecting a black ball from a box: [tex]\frac{1}{2}[/tex]
Probability of selecting a black ball from a box: [tex]\frac{2}{3}[/tex]
To determine: the likelihood that the marble is black.
Solution:
The likelihood that the marble being black is equal to
[tex]\frac{1}{2} (\frac{1}{2} ) + \frac{1}{2} (\frac{2}{3} )\\= \frac{7}{12}[/tex]
Learn mor about probability here:
https://brainly.com/question/14595377
#SPJ4
What is the area of this polygon?
Enter your answer in the box.
units?
Check the picture below.
so the polygon is really just a 5x7 rectangle with a triangle that has a base of 7 units(vertically) and a height of 2 units.
[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{rectangle}{(5)(7)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(7)(2)}}\implies 35~~ + ~~7\implies \text{\LARGE 42}~units^2[/tex]
if the true population proportion for a sample size of 200 is found to be 0.2, then the standard error will be
The correct option is SE is 0.04. In statistics, a sample proportion is a statistic that represents the proportion of individuals in a sample who have a particular characteristic or belong to a certain category.
The standard error of the sample proportion can be calculated as follows:
SE = sqrt(p * (1 - p) / n)
Where p is the sample proportion and n is the sample size. In this case, the sample proportion is 0.2, and the sample size is 200. So, plugging these values into the formula, we get:
SE = sqrt(0.2 * (1 - 0.2) / 200)
SE = sqrt(0.16 / 200)
SE = 0.04
To learn more sample proportion, visit here
https://brainly.com/question/29912751
#SPJ4
Determine whether segments with lengths of 29, 19, and 29 form a triangle. If so, classify the triangle as acute, right, or obtuse.
Answer:
if the angle has the arrow on top pointing straight up thats a right angle if it is leaning towards the left instead it is obtuse and if is getting closer to the right side it is acute.
Step-by-step explanation:
i can't tell you anything else if there is no picture to base this question.
5x +6y = 4
10x+12y = 8
What is the system of equation is it no solution, one solution, or infinitely many solutions?
The equation 5x + 6y = 4, 10x + 12y = 8 has infinitely many solution.
How to solve system of equation?System of equation can be solved using elimination method, substitution method and graphical method.
Therefore, let's solve the system of equation using elimination method.
5x + 6y = 4
10x + 12y = 8
multiply equation(i) by 2
Hence,
10x + 12y = 8
10x + 12y = 8
subtract the equations
0 = 0
Therefore, the equation has infinitely many solution.
learn more on equation here: https://brainly.com/question/29173348
#SPJ1
what is 3 1/2x - 5 1/2x,x=2/5
Answer:
[tex]-\dfrac{4}{5}[/tex]
Step-by-step explanation:
We have the following expression
[tex]3 \;\dfrac{1}{2} x - 5\;\dfrac{1}{2}x[/tex]
and asked to evaluate this expression at [tex]\[x = {2\over\displaystyle 5\][/tex]
First convert [tex]3 \; \dfrac{1}{2}[/tex] and [tex]5 \; \dfrac{1}{2}[/tex] to mixed fractions
[tex]3 \; \dfrac{1}{2} = \dfrac{3 \times 2 + 1}{2} = \dfrac{7}{2}\\[/tex]
[tex]5 \; \dfrac{1}{2} = \dfrac{5 \times 2 + 1}{2} = \dfrac{11}{2}[/tex]
Therefore
[tex]3 \;\dfrac{1}{2} x - 5\;\dfrac{1}{2}x\\\\= \dfrac{7}{2}x - \dfrac{11}{2}x\\\\= \dfrac{7 - 11}{2} x\\\\= -\dfrac{4}{2}x \\\\= -2x\\\\[/tex]
[tex]\mathrm{For \;x =\dfrac{2}{5}},\\\\= -2x \\= - 2 \times \dfrac{2}{5}\\\\= -\dfrac{4}{5}[/tex]
1) Operaciones con números escritos en notación científica
a) Después de reunir información, Kara decidió sumar algunas distancias. Decidió sumas la
distancia de la Tierra a Saturno con la distancia de la Tierra a Júpiter.
Aquí está lo que escribió.
5.95 × 108 + 8.87 × 108
¿Sabes cuál es el resultado?
We can write the equivalent expression as -
{5.95 × 10⁸ + 8.87 × 10⁸} = {10⁸ x 14.82}.
What are algebraic expressions?In mathematics, an expression or mathematical expression is combination of terms both constants and variables. For example -
23 + 54
2x + 5
3x + 5y + z
Given is that after gathering information, Kara decided to add up some distances. She decided to add the distance from Earth to Saturn with the distance from Earth to Jupiter. He wrote -
5.95 × 10⁸ + 8.87 × 10⁸
The given expression is -
5.95 × 10⁸ + 8.87 × 10⁸
10⁸ x (5.95 + 8.87)
10⁸ x 14.82
Therefore, we can write the equivalent expression as -
5.95 × 10⁸ + 8.87 × 10⁸ = 10⁸ x 14.82.
To solve more questions on functions & expressions, visit the link below
brainly.com/question/17613163
#SPJ9
{Question in english -
1) Operations with numbers written in scientific notation
a) After gathering information, Kara decided to add up some distances. decided to add the distance from Earth to Saturn with the distance from Earth to Jupiter. Here is what he wrote.
5.95×108 + 8.87×108
Do you know what the result is?}
megan wants to test her assumption on the amount of sleep students are getting. she decides to focus her efforts on examining if students are getting less than eight hours of sleep. what should megan state for the null hypothesis and alternative hypothesis? a.) null hypothesis: alternative hypothesis: b.) null hypothesis: alternative hypothesis: c.) null hypothesis: alternative hypothesis: d.) null hypothesis: alternative hypothesis:
To state the null hypothesis and alternative hypothesis for Megan's test, we need to know what type of data she will be collecting and what type of test she will be conducting.
Assuming she will be collecting data on the number of hours of sleep students are getting and conducting a one-tailed hypothesis test, the following are possible null and alternative hypotheses:
a.) Null hypothesis: The average amount of sleep students are getting is equal to or greater than eight hours per night.
Alternative hypothesis: The average amount of sleep students are getting is less than eight hours per night.
b.) Null hypothesis: Less than or equal to 50% of students are getting less than eight hours of sleep per night.
Alternative hypothesis: More than 50% of students are getting less than eight hours of sleep per night.
c.) Null hypothesis: There is no difference in the proportion of students getting less than eight hours of sleep between two groups (e.g., males vs. females, freshmen vs. seniors, etc.).
Alternative hypothesis: There is a difference in the proportion of students getting less than eight hours of sleep between two groups.
d.) Null hypothesis: The number of students getting less than eight hours of sleep is equal to or greater than a certain value (e.g., 30%).
Alternative hypothesis: The number of students getting less than eight hours of sleep is less than the specified value.
Note that in each case, the null hypothesis represents the status quo or the default assumption, while the alternative hypothesis represents Megan's research question or hypothesis. The choice of null and alternative hypotheses depends on the research question, the data being collected, and the type of hypothesis test being conducted.
To learn more about null hypothesis here:
https://brainly.com/question/28920252
#SPJ4
(Right answers only. please help thanks)
A quilter created the following shape to use in a block for a new quilt.
A six-sided figure with a large base of 10 and three-fifths inches. The side to the right of the base is 6 inches. The small side parallel to the base is 4 and one-fifth inches. There are two sides that form a point at a right angle. The smaller is 4 inches, and the larger is 5 inches.
What is the area of the shape for the quilt block?
73 3/5 in
41 4/5 in
83 3/5 in
147 1/5 in
Answer: 83 3/5
Step-by-step explanation:
hope this helps !! :3
5. Find tn for the geometric sequence where t3 = 24 and t9 = 1536. Why are there 2 answers? (4 marks)
Answer: A geometric sequence is a sequence of numbers such that the ratio of any two consecutive terms is constant. Let's call the common ratio "r". We can use this property to find "r" and then calculate other terms in the sequence.
Given that t3 = 24 and t9 = 1536, we can use the formula for the nth term in a geometric sequence: tn = t1 * r^(n-1), where t1 is the first term in the sequence.
Since we know t3 and t9, we can find r by dividing t9 by t3:
r = t9/t3 = 1536/24 = 64
Now that we have found "r", we can use it to find t1 by dividing t3 by r^(3-1):
t1 = t3 / r^(3-1) = 24 / 64^(3-1) = 24 / 64 = 3/2
Now that we know t1 and r, we can find any term in the sequence by using the formula: tn = t1 * r^(n-1).
Therefore, there are two possible sequences with two different first terms:
Sequence 1: t1 = 3/2, r = 64
Sequence 2: t1 = -3/2, r = -64
These are the two possible geometric sequences that satisfy the conditions t3 = 24 and t9 = 1536.
Step-by-step explanation:
data with 860 observations are drawn from a bell-shaped distribution with a mean of 76 and a standard deviation of 18. approximately how many observations are more than 112? (round your answer to the nearest whole number.)
In the given case where 860 observations are drawn from a bell-shaped distribution, there are 2 observations of more than 112.
Total number of observations = 860
Mean of the observations = 76
Standard deviation = 18
The amount of standard deviations by which the value of a raw score differs from or differs above the mean value of what is observed or measured is known as the z score or standard score in the z test. The z-score calculates how far an X-score deviates from the mean by standard deviations. Calculating the observations utilizing the Z- score -
Z = X - u/a
Calculating the observations -
Where X = 112 u = 76 and a = 18
Z = 112 - 76/18
= 36/18
= 2
Read more about z-score on:
brainly.com/question/28000192
#SPJ4
There are eight groups of students, each working on a science project in the gym. Each group has the same number of students. Mr. Davids asks for 44 students from each group come with him to get more supplies. Now there are a total of 5656 students in the gym.
a. Write an equation to represent this situation, where xx represents the number of students in each group.
Preview
b. How many students are in each group? Simplify your answer completely.
Answer:
58585
Step-by-step explanation:
i know
you leave a 20% tip on your $70 dinner bill. how much was the tip
Answer: The tip is $14.00
Step-by-step explanation: 20% of 70 is 14.
What is the solution to the system of equations?
x + 3y + 2z = 8
3x + y + 3z = -10
-2x - 2y -z = 10
Answer:
x = 8 - 3y - 2z
Step-by-step explanation:
Step-by-step explanation:
x + 3y + 2z = 8
3x + y + 3z = -10
-2x - 2y - z = 10
we solve this by eliminating variables or expressing sine variables by others, and then solve for the remaining one. with that value we then cancer back to solve for the other variables.
in our case the easiest way is the elimination via combinations of equations.
let's first multiply equating 1 by -3 and then add that to equation 2 :
-3x - 9y - 6z = -24
3x + y + 3z = -10
----------------------------
0 - 8y - 3z = -34
8y + 3z = 34
then multiply equation 1 by 2 and add it to equation 3 :
2x + 6y + 4z = 16
-2x - 2y - z = 10
--------------------------
0 4y + 3z = 26
now we subtract this result from the previous result :
8y + 3z = 34
- 4y + 3z = 26
----------------------------
4y 0 = 8
y = 8/4 = 2
4×2 + 3z = 26
3z = 18
z = 18/3 = 6
x + 3×2 + 2×6 = 8
x = -10
so,
x = -10
y = 2
z = 6
HELPP PLSSS
Factor the polynomial.
x²+2x² +14x+7x²
Answer:
2x(5x+7)
Step-by-step explanation:
[tex]x^2+2x^2+14x+7x^2\\=10x^2+14x\\=2x(5x+7)[/tex]
the mariana trench is about 11km deep. mount everest is about 29,000 ft high. what is the total height change from the top of mount everest to the bottom of the mariana trench, expressed in miles?
Using unit conversions the total height change from the top of mount Everest to the bottom of the Mariana trench is 12.3 miles
We know that 1 km = 0.62136 miles and 1 foot = 0.000189 miles
Depth of Mariana Trench (d) = 11 km = 11 × 0.62136
= 6.835 miles
Height of Mount Everest (h) = 29000 ft = 29000 × 0.000189
= 5.492 miles
Therefore the total height difference top of Mount Everest and to bottom of the Mariana Trench is given by
H = Depth of Mariana Trench + Height of Mount Everest
H = d + h
H = 6.835 miles + 5.492 miles
H = 12.327 miles
H = 12.3 miles
To learn more about unit conversions here:
brainly.com/question/19420601
#SPJ4
How many 3-letter words can we make from the letters A, B, C, and D, if we are allowed to repeat letters, and we must use the letter A at least once?
Answer:
37
Step-by-step explanation:
AAA 1 way
AAB, AAC, AAD 3 ways each 3*3=9 ways
ABB, ACC, ADD 3 ways each 3*3=9 ways
ABC, ABD, ACD 3*2=6 ways each 3*6=18ways
1+9+9+18 = 37 ways
